diff --git a/packages/babel-parser/src/parser/error-message.js b/packages/babel-parser/src/parser/error-message.js
index 90c0b1025e0f..a9d609930b1d 100644
--- a/packages/babel-parser/src/parser/error-message.js
+++ b/packages/babel-parser/src/parser/error-message.js
@@ -77,6 +77,8 @@ export const ErrorMessages = Object.freeze({
   InvalidLhs: "Invalid left-hand side in %0",
   InvalidLhsBinding: "Binding invalid left-hand side in %0",
   InvalidNumber: "Invalid number",
+  InvalidOrMissingExponent:
+    "Floating-point numbers require a valid exponent after the 'e'",
   InvalidOrUnexpectedToken: "Unexpected character '%0'",
   InvalidParenthesizedAssignment: "Invalid parenthesized assignment pattern",
   InvalidPrivateFieldResolution: "Private name #%0 is not defined",
diff --git a/packages/babel-parser/src/tokenizer/index.js b/packages/babel-parser/src/tokenizer/index.js
index cbc0efab0fe8..573db84a3273 100644
--- a/packages/babel-parser/src/tokenizer/index.js
+++ b/packages/babel-parser/src/tokenizer/index.js
@@ -1149,7 +1149,9 @@ export default class Tokenizer extends ParserErrors {
       if (next === charCodes.plusSign || next === charCodes.dash) {
         ++this.state.pos;
       }
-      if (this.readInt(10) === null) this.raise(start, Errors.InvalidNumber);
+      if (this.readInt(10) === null) {
+        this.raise(start, Errors.InvalidOrMissingExponent);
+      }
       isFloat = true;
       hasExponent = true;
       next = this.input.charCodeAt(this.state.pos);
diff --git a/packages/babel-parser/test/fixtures/core/uncategorised/349/output.json b/packages/babel-parser/test/fixtures/core/uncategorised/349/output.json
index b2d2e40318a4..6afcaf3f5045 100644
--- a/packages/babel-parser/test/fixtures/core/uncategorised/349/output.json
+++ b/packages/babel-parser/test/fixtures/core/uncategorised/349/output.json
@@ -2,7 +2,7 @@
   "type": "File",
   "start":0,"end":2,"loc":{"start":{"line":1,"column":0},"end":{"line":1,"column":2}},
   "errors": [
-    "SyntaxError: Invalid number (1:0)"
+    "SyntaxError: Floating-point numbers require a valid exponent after the 'e' (1:0)"
   ],
   "program": {
     "type": "Program",
diff --git a/packages/babel-parser/test/fixtures/core/uncategorised/350/output.json b/packages/babel-parser/test/fixtures/core/uncategorised/350/output.json
index 1591ec979e44..34027472096c 100644
--- a/packages/babel-parser/test/fixtures/core/uncategorised/350/output.json
+++ b/packages/babel-parser/test/fixtures/core/uncategorised/350/output.json
@@ -2,7 +2,7 @@
   "type": "File",
   "start":0,"end":3,"loc":{"start":{"line":1,"column":0},"end":{"line":1,"column":3}},
   "errors": [
-    "SyntaxError: Invalid number (1:0)"
+    "SyntaxError: Floating-point numbers require a valid exponent after the 'e' (1:0)"
   ],
   "program": {
     "type": "Program",
diff --git a/packages/babel-parser/test/fixtures/core/uncategorised/351/output.json b/packages/babel-parser/test/fixtures/core/uncategorised/351/output.json
index 42c6c5a67aff..666fcca21213 100644
--- a/packages/babel-parser/test/fixtures/core/uncategorised/351/output.json
+++ b/packages/babel-parser/test/fixtures/core/uncategorised/351/output.json
@@ -2,7 +2,7 @@
   "type": "File",
   "start":0,"end":3,"loc":{"start":{"line":1,"column":0},"end":{"line":1,"column":3}},
   "errors": [
-    "SyntaxError: Invalid number (1:0)"
+    "SyntaxError: Floating-point numbers require a valid exponent after the 'e' (1:0)"
   ],
   "program": {
     "type": "Program",
diff --git a/packages/babel-parser/test/fixtures/esprima/invalid-syntax/migrated_0004/output.json b/packages/babel-parser/test/fixtures/esprima/invalid-syntax/migrated_0004/output.json
index b2d2e40318a4..6afcaf3f5045 100644
--- a/packages/babel-parser/test/fixtures/esprima/invalid-syntax/migrated_0004/output.json
+++ b/packages/babel-parser/test/fixtures/esprima/invalid-syntax/migrated_0004/output.json
@@ -2,7 +2,7 @@
   "type": "File",
   "start":0,"end":2,"loc":{"start":{"line":1,"column":0},"end":{"line":1,"column":2}},
   "errors": [
-    "SyntaxError: Invalid number (1:0)"
+    "SyntaxError: Floating-point numbers require a valid exponent after the 'e' (1:0)"
   ],
   "program": {
     "type": "Program",
diff --git a/packages/babel-parser/test/fixtures/esprima/invalid-syntax/migrated_0005/output.json b/packages/babel-parser/test/fixtures/esprima/invalid-syntax/migrated_0005/output.json
index 1591ec979e44..34027472096c 100644
--- a/packages/babel-parser/test/fixtures/esprima/invalid-syntax/migrated_0005/output.json
+++ b/packages/babel-parser/test/fixtures/esprima/invalid-syntax/migrated_0005/output.json
@@ -2,7 +2,7 @@
   "type": "File",
   "start":0,"end":3,"loc":{"start":{"line":1,"column":0},"end":{"line":1,"column":3}},
   "errors": [
-    "SyntaxError: Invalid number (1:0)"
+    "SyntaxError: Floating-point numbers require a valid exponent after the 'e' (1:0)"
   ],
   "program": {
     "type": "Program",
diff --git a/packages/babel-parser/test/fixtures/esprima/invalid-syntax/migrated_0006/output.json b/packages/babel-parser/test/fixtures/esprima/invalid-syntax/migrated_0006/output.json
index 42c6c5a67aff..666fcca21213 100644
--- a/packages/babel-parser/test/fixtures/esprima/invalid-syntax/migrated_0006/output.json
+++ b/packages/babel-parser/test/fixtures/esprima/invalid-syntax/migrated_0006/output.json
@@ -2,7 +2,7 @@
   "type": "File",
   "start":0,"end":3,"loc":{"start":{"line":1,"column":0},"end":{"line":1,"column":3}},
   "errors": [
-    "SyntaxError: Invalid number (1:0)"
+    "SyntaxError: Floating-point numbers require a valid exponent after the 'e' (1:0)"
   ],
   "program": {
     "type": "Program",