diff --git a/packages/babel-parser/src/plugins/jsx/index.js b/packages/babel-parser/src/plugins/jsx/index.js
index 6344996fe4f2..f65b28476cd0 100644
--- a/packages/babel-parser/src/plugins/jsx/index.js
+++ b/packages/babel-parser/src/plugins/jsx/index.js
@@ -204,7 +204,7 @@ export default (superClass: Class<Parser>): Class<Parser> =>
           /* allowNumSeparator */ "bail",
         );
         if (
-          codePoint &&
+          codePoint !== null &&
           this.codePointAtPos(this.state.pos) === charCodes.semicolon
         ) {
           ++this.state.pos;
diff --git a/packages/babel-parser/test/fixtures/jsx/html-entities/code-point/input.js b/packages/babel-parser/test/fixtures/jsx/html-entities/code-point/input.js
index 1578ea516db1..9867befe0ece 100644
--- a/packages/babel-parser/test/fixtures/jsx/html-entities/code-point/input.js
+++ b/packages/babel-parser/test/fixtures/jsx/html-entities/code-point/input.js
@@ -3,4 +3,5 @@
     &#xABC;
     &#00000000000000000000001234;
     &#x0000000000000000000000ABC;
+    &#0000;
 </a>
diff --git a/packages/babel-parser/test/fixtures/jsx/html-entities/code-point/output.json b/packages/babel-parser/test/fixtures/jsx/html-entities/code-point/output.json
index 727c467c1a42..c53f68eb4fff 100644
--- a/packages/babel-parser/test/fixtures/jsx/html-entities/code-point/output.json
+++ b/packages/babel-parser/test/fixtures/jsx/html-entities/code-point/output.json
@@ -1,18 +1,18 @@
 {
   "type": "File",
-  "start":0,"end":100,"loc":{"start":{"line":1,"column":0,"index":0},"end":{"line":6,"column":4,"index":100}},
+  "start":0,"end":112,"loc":{"start":{"line":1,"column":0,"index":0},"end":{"line":7,"column":4,"index":112}},
   "program": {
     "type": "Program",
-    "start":0,"end":100,"loc":{"start":{"line":1,"column":0,"index":0},"end":{"line":6,"column":4,"index":100}},
+    "start":0,"end":112,"loc":{"start":{"line":1,"column":0,"index":0},"end":{"line":7,"column":4,"index":112}},
     "sourceType": "script",
     "interpreter": null,
     "body": [
       {
         "type": "ExpressionStatement",
-        "start":0,"end":100,"loc":{"start":{"line":1,"column":0,"index":0},"end":{"line":6,"column":4,"index":100}},
+        "start":0,"end":112,"loc":{"start":{"line":1,"column":0,"index":0},"end":{"line":7,"column":4,"index":112}},
         "expression": {
           "type": "JSXElement",
-          "start":0,"end":100,"loc":{"start":{"line":1,"column":0,"index":0},"end":{"line":6,"column":4,"index":100}},
+          "start":0,"end":112,"loc":{"start":{"line":1,"column":0,"index":0},"end":{"line":7,"column":4,"index":112}},
           "openingElement": {
             "type": "JSXOpeningElement",
             "start":0,"end":3,"loc":{"start":{"line":1,"column":0,"index":0},"end":{"line":1,"column":3,"index":3}},
@@ -26,22 +26,22 @@
           },
           "closingElement": {
             "type": "JSXClosingElement",
-            "start":96,"end":100,"loc":{"start":{"line":6,"column":0,"index":96},"end":{"line":6,"column":4,"index":100}},
+            "start":108,"end":112,"loc":{"start":{"line":7,"column":0,"index":108},"end":{"line":7,"column":4,"index":112}},
             "name": {
               "type": "JSXIdentifier",
-              "start":98,"end":99,"loc":{"start":{"line":6,"column":2,"index":98},"end":{"line":6,"column":3,"index":99}},
+              "start":110,"end":111,"loc":{"start":{"line":7,"column":2,"index":110},"end":{"line":7,"column":3,"index":111}},
               "name": "a"
             }
           },
           "children": [
             {
               "type": "JSXText",
-              "start":3,"end":96,"loc":{"start":{"line":1,"column":3,"index":3},"end":{"line":6,"column":0,"index":96}},
+              "start":3,"end":108,"loc":{"start":{"line":1,"column":3,"index":3},"end":{"line":7,"column":0,"index":108}},
               "extra": {
-                "rawValue": "\n    Ӓ\n    ઼\n    Ӓ\n    ઼\n",
-                "raw": "\n    &#1234;\n    &#xABC;\n    &#00000000000000000000001234;\n    &#x0000000000000000000000ABC;\n"
+                "rawValue": "\n    Ӓ\n    ઼\n    Ӓ\n    ઼\n    \u0000\n",
+                "raw": "\n    &#1234;\n    &#xABC;\n    &#00000000000000000000001234;\n    &#x0000000000000000000000ABC;\n    &#0000;\n"
               },
-              "value": "\n    Ӓ\n    ઼\n    Ӓ\n    ઼\n"
+              "value": "\n    Ӓ\n    ઼\n    Ӓ\n    ઼\n    \u0000\n"
             }
           ]
         }