diff --git a/packages/babel-parser/src/parser/expression.js b/packages/babel-parser/src/parser/expression.js
index 2e50be642368..dd7641990a06 100644
--- a/packages/babel-parser/src/parser/expression.js
+++ b/packages/babel-parser/src/parser/expression.js
@@ -2100,7 +2100,9 @@ export default class ExpressionParser extends LValParser {
   isSimpleReference(expression: N.Expression): boolean {
     switch (expression.type) {
       case "MemberExpression":
-        return this.isSimpleReference(expression.object);
+        return (
+          !expression.computed && this.isSimpleReference(expression.object)
+        );
       case "Identifier":
         return true;
       default:
diff --git a/packages/babel-parser/test/fixtures/experimental/pipeline-operator/proposal-smart-bare-style,-function-calls,-single,-computed/options.json b/packages/babel-parser/test/fixtures/experimental/pipeline-operator/proposal-smart-bare-style,-function-calls,-single,-computed/options.json
deleted file mode 100644
index 17e4e327bbad..000000000000
--- a/packages/babel-parser/test/fixtures/experimental/pipeline-operator/proposal-smart-bare-style,-function-calls,-single,-computed/options.json
+++ /dev/null
@@ -1,3 +0,0 @@
-{
-  "plugins": [["pipelineOperator", { "proposal": "smart" }]]
-}
diff --git a/packages/babel-parser/test/fixtures/experimental/pipeline-operator/proposal-smart-bare-style,-function-calls,-single,-computed/output.json b/packages/babel-parser/test/fixtures/experimental/pipeline-operator/proposal-smart-bare-style,-function-calls,-single,-computed/output.json
deleted file mode 100644
index 540ce0ba4002..000000000000
--- a/packages/babel-parser/test/fixtures/experimental/pipeline-operator/proposal-smart-bare-style,-function-calls,-single,-computed/output.json
+++ /dev/null
@@ -1,148 +0,0 @@
-{
-  "type": "File",
-  "start": 0,
-  "end": 13,
-  "loc": {
-    "start": {
-      "line": 1,
-      "column": 0
-    },
-    "end": {
-      "line": 1,
-      "column": 13
-    }
-  },
-  "program": {
-    "type": "Program",
-    "start": 0,
-    "end": 13,
-    "loc": {
-      "start": {
-        "line": 1,
-        "column": 0
-      },
-      "end": {
-        "line": 1,
-        "column": 13
-      }
-    },
-    "sourceType": "script",
-    "interpreter": null,
-    "body": [
-      {
-        "type": "ExpressionStatement",
-        "start": 0,
-        "end": 13,
-        "loc": {
-          "start": {
-            "line": 1,
-            "column": 0
-          },
-          "end": {
-            "line": 1,
-            "column": 13
-          }
-        },
-        "expression": {
-          "type": "BinaryExpression",
-          "start": 0,
-          "end": 13,
-          "loc": {
-            "start": {
-              "line": 1,
-              "column": 0
-            },
-            "end": {
-              "line": 1,
-              "column": 13
-            }
-          },
-          "left": {
-            "type": "Identifier",
-            "start": 0,
-            "end": 5,
-            "loc": {
-              "start": {
-                "line": 1,
-                "column": 0
-              },
-              "end": {
-                "line": 1,
-                "column": 5
-              },
-              "identifierName": "value"
-            },
-            "name": "value"
-          },
-          "operator": "|>",
-          "right": {
-            "type": "PipelineBareFunction",
-            "start": 9,
-            "end": 13,
-            "loc": {
-              "start": {
-                "line": 1,
-                "column": 9
-              },
-              "end": {
-                "line": 1,
-                "column": 13
-              }
-            },
-            "callee": {
-              "type": "MemberExpression",
-              "start": 9,
-              "end": 13,
-              "loc": {
-                "start": {
-                  "line": 1,
-                  "column": 9
-                },
-                "end": {
-                  "line": 1,
-                  "column": 13
-                }
-              },
-              "object": {
-                "type": "Identifier",
-                "start": 9,
-                "end": 10,
-                "loc": {
-                  "start": {
-                    "line": 1,
-                    "column": 9
-                  },
-                  "end": {
-                    "line": 1,
-                    "column": 10
-                  },
-                  "identifierName": "a"
-                },
-                "name": "a"
-              },
-              "property": {
-                "type": "Identifier",
-                "start": 11,
-                "end": 12,
-                "loc": {
-                  "start": {
-                    "line": 1,
-                    "column": 11
-                  },
-                  "end": {
-                    "line": 1,
-                    "column": 12
-                  },
-                  "identifierName": "b"
-                },
-                "name": "b"
-              },
-              "computed": true
-            }
-          }
-        }
-      }
-    ],
-    "directives": []
-  }
-}
\ No newline at end of file
diff --git a/packages/babel-parser/test/fixtures/experimental/pipeline-operator/proposal-smart-bare-style,-function-calls,-single,-computed/input.js b/packages/babel-parser/test/fixtures/experimental/pipeline-operator/proposal-smart-error,-topic-style,-computed,-no-topic-reference/input.js
similarity index 100%
rename from packages/babel-parser/test/fixtures/experimental/pipeline-operator/proposal-smart-bare-style,-function-calls,-single,-computed/input.js
rename to packages/babel-parser/test/fixtures/experimental/pipeline-operator/proposal-smart-error,-topic-style,-computed,-no-topic-reference/input.js
diff --git a/packages/babel-parser/test/fixtures/experimental/pipeline-operator/proposal-smart-error,-topic-style,-computed,-no-topic-reference/options.json b/packages/babel-parser/test/fixtures/experimental/pipeline-operator/proposal-smart-error,-topic-style,-computed,-no-topic-reference/options.json
new file mode 100644
index 000000000000..7a4451381c91
--- /dev/null
+++ b/packages/babel-parser/test/fixtures/experimental/pipeline-operator/proposal-smart-error,-topic-style,-computed,-no-topic-reference/options.json
@@ -0,0 +1,4 @@
+{
+  "plugins": [["pipelineOperator", { "proposal": "smart" }]],
+  "throws": "Pipeline is in topic style but does not use topic reference (1:9)"
+}