diff --git a/packages/babel-parser/src/plugins/typescript/index.ts b/packages/babel-parser/src/plugins/typescript/index.ts
index eeab6202bad0..645d1daa5503 100644
--- a/packages/babel-parser/src/plugins/typescript/index.ts
+++ b/packages/babel-parser/src/plugins/typescript/index.ts
@@ -2493,10 +2493,11 @@ export default (superClass: {
 
           const tokenType = this.state.type;
           if (
-            // a<b>>c is not (a<b>)>c, but a<(b>>c)
-            tokenType === tt.gt ||
-            // a<b>>>c is not (a<b>)>>c, but a<(b>>>c)
-            tokenType === tt.bitShiftR ||
+            (this.state.start === this.state.lastTokStart + 1 &&
+              // a<b>>c is not (a<b>)>c, but a<(b>>c)
+              (tokenType === tt.gt ||
+                // a<b>>>c is not (a<b>)>>c, but a<(b>>>c)
+                tokenType === tt.bitShiftR)) ||
             // a<b>c is (a<b)>c
             (tokenType !== tt.parenL &&
               tokenCanStartExpression(tokenType) &&
diff --git a/packages/babel-parser/test/fixtures/typescript/type-arguments/instantiation-expression-binary-operator-2/input.ts b/packages/babel-parser/test/fixtures/typescript/type-arguments/instantiation-expression-binary-operator-2/input.ts
new file mode 100644
index 000000000000..929f46c802e9
--- /dev/null
+++ b/packages/babel-parser/test/fixtures/typescript/type-arguments/instantiation-expression-binary-operator-2/input.ts
@@ -0,0 +1 @@
+a<b> > c;
diff --git a/packages/babel-parser/test/fixtures/typescript/type-arguments/instantiation-expression-binary-operator-2/output.json b/packages/babel-parser/test/fixtures/typescript/type-arguments/instantiation-expression-binary-operator-2/output.json
new file mode 100644
index 000000000000..ab436ec84967
--- /dev/null
+++ b/packages/babel-parser/test/fixtures/typescript/type-arguments/instantiation-expression-binary-operator-2/output.json
@@ -0,0 +1,51 @@
+{
+  "type": "File",
+  "start":0,"end":9,"loc":{"start":{"line":1,"column":0,"index":0},"end":{"line":1,"column":9,"index":9}},
+  "program": {
+    "type": "Program",
+    "start":0,"end":9,"loc":{"start":{"line":1,"column":0,"index":0},"end":{"line":1,"column":9,"index":9}},
+    "sourceType": "module",
+    "interpreter": null,
+    "body": [
+      {
+        "type": "ExpressionStatement",
+        "start":0,"end":9,"loc":{"start":{"line":1,"column":0,"index":0},"end":{"line":1,"column":9,"index":9}},
+        "expression": {
+          "type": "BinaryExpression",
+          "start":0,"end":8,"loc":{"start":{"line":1,"column":0,"index":0},"end":{"line":1,"column":8,"index":8}},
+          "left": {
+            "type": "TSInstantiationExpression",
+            "start":0,"end":4,"loc":{"start":{"line":1,"column":0,"index":0},"end":{"line":1,"column":4,"index":4}},
+            "expression": {
+              "type": "Identifier",
+              "start":0,"end":1,"loc":{"start":{"line":1,"column":0,"index":0},"end":{"line":1,"column":1,"index":1},"identifierName":"a"},
+              "name": "a"
+            },
+            "typeParameters": {
+              "type": "TSTypeParameterInstantiation",
+              "start":1,"end":4,"loc":{"start":{"line":1,"column":1,"index":1},"end":{"line":1,"column":4,"index":4}},
+              "params": [
+                {
+                  "type": "TSTypeReference",
+                  "start":2,"end":3,"loc":{"start":{"line":1,"column":2,"index":2},"end":{"line":1,"column":3,"index":3}},
+                  "typeName": {
+                    "type": "Identifier",
+                    "start":2,"end":3,"loc":{"start":{"line":1,"column":2,"index":2},"end":{"line":1,"column":3,"index":3},"identifierName":"b"},
+                    "name": "b"
+                  }
+                }
+              ]
+            }
+          },
+          "operator": ">",
+          "right": {
+            "type": "Identifier",
+            "start":7,"end":8,"loc":{"start":{"line":1,"column":7,"index":7},"end":{"line":1,"column":8,"index":8},"identifierName":"c"},
+            "name": "c"
+          }
+        }
+      }
+    ],
+    "directives": []
+  }
+}
diff --git a/packages/babel-parser/test/fixtures/typescript/type-arguments/instantiation-expression-binary-operator-3/input.ts b/packages/babel-parser/test/fixtures/typescript/type-arguments/instantiation-expression-binary-operator-3/input.ts
new file mode 100644
index 000000000000..5b90b10a4511
--- /dev/null
+++ b/packages/babel-parser/test/fixtures/typescript/type-arguments/instantiation-expression-binary-operator-3/input.ts
@@ -0,0 +1 @@
+a<b> >> c;
diff --git a/packages/babel-parser/test/fixtures/typescript/type-arguments/instantiation-expression-binary-operator-3/output.json b/packages/babel-parser/test/fixtures/typescript/type-arguments/instantiation-expression-binary-operator-3/output.json
new file mode 100644
index 000000000000..2b5e51509615
--- /dev/null
+++ b/packages/babel-parser/test/fixtures/typescript/type-arguments/instantiation-expression-binary-operator-3/output.json
@@ -0,0 +1,51 @@
+{
+  "type": "File",
+  "start":0,"end":10,"loc":{"start":{"line":1,"column":0,"index":0},"end":{"line":1,"column":10,"index":10}},
+  "program": {
+    "type": "Program",
+    "start":0,"end":10,"loc":{"start":{"line":1,"column":0,"index":0},"end":{"line":1,"column":10,"index":10}},
+    "sourceType": "module",
+    "interpreter": null,
+    "body": [
+      {
+        "type": "ExpressionStatement",
+        "start":0,"end":10,"loc":{"start":{"line":1,"column":0,"index":0},"end":{"line":1,"column":10,"index":10}},
+        "expression": {
+          "type": "BinaryExpression",
+          "start":0,"end":9,"loc":{"start":{"line":1,"column":0,"index":0},"end":{"line":1,"column":9,"index":9}},
+          "left": {
+            "type": "TSInstantiationExpression",
+            "start":0,"end":4,"loc":{"start":{"line":1,"column":0,"index":0},"end":{"line":1,"column":4,"index":4}},
+            "expression": {
+              "type": "Identifier",
+              "start":0,"end":1,"loc":{"start":{"line":1,"column":0,"index":0},"end":{"line":1,"column":1,"index":1},"identifierName":"a"},
+              "name": "a"
+            },
+            "typeParameters": {
+              "type": "TSTypeParameterInstantiation",
+              "start":1,"end":4,"loc":{"start":{"line":1,"column":1,"index":1},"end":{"line":1,"column":4,"index":4}},
+              "params": [
+                {
+                  "type": "TSTypeReference",
+                  "start":2,"end":3,"loc":{"start":{"line":1,"column":2,"index":2},"end":{"line":1,"column":3,"index":3}},
+                  "typeName": {
+                    "type": "Identifier",
+                    "start":2,"end":3,"loc":{"start":{"line":1,"column":2,"index":2},"end":{"line":1,"column":3,"index":3},"identifierName":"b"},
+                    "name": "b"
+                  }
+                }
+              ]
+            }
+          },
+          "operator": ">>",
+          "right": {
+            "type": "Identifier",
+            "start":8,"end":9,"loc":{"start":{"line":1,"column":8,"index":8},"end":{"line":1,"column":9,"index":9},"identifierName":"c"},
+            "name": "c"
+          }
+        }
+      }
+    ],
+    "directives": []
+  }
+}