diff --git a/mlir/lib/Conversion/FuncToLLVM/FuncToLLVM.cpp b/mlir/lib/Conversion/FuncToLLVM/FuncToLLVM.cpp
--- a/mlir/lib/Conversion/FuncToLLVM/FuncToLLVM.cpp
+++ b/mlir/lib/Conversion/FuncToLLVM/FuncToLLVM.cpp
@@ -208,6 +208,13 @@
       wrapperType, LLVM::Linkage::External, /*dsoLocal*/ false,
       /*cconv*/ LLVM::CConv::C, attributes);
 
+  // Unless set explicitly in the original op, set the linkage of the new op to
+  // internal: this op used to be just a declaration to an externally defined
+  // function. The wrapper that we make out of it, however, should only be
+  // visible in this module.
+  if (!funcOp->hasAttr(linkageAttrName))
+    newFuncOp.setLinkage(LLVM::Linkage::Internal);
+
   builder.setInsertionPointToStart(newFuncOp.addEntryBlock());
 
   // Get a ValueRange containing arguments.
diff --git a/mlir/test/Conversion/FuncToLLVM/emit-c-wrappers-for-external-functions.mlir b/mlir/test/Conversion/FuncToLLVM/emit-c-wrappers-for-external-functions.mlir
--- a/mlir/test/Conversion/FuncToLLVM/emit-c-wrappers-for-external-functions.mlir
+++ b/mlir/test/Conversion/FuncToLLVM/emit-c-wrappers-for-external-functions.mlir
@@ -1,38 +1,38 @@
 // RUN: mlir-opt -llvm-request-c-wrappers -convert-func-to-llvm='use-opaque-pointers=1' %s | FileCheck %s
 
-// CHECK: llvm.func @res_attrs_with_memref_return() -> (!llvm.struct{{.*}} {test.returnOne})
+// CHECK: llvm.func internal @res_attrs_with_memref_return() -> (!llvm.struct{{.*}} {test.returnOne})
 // CHECK-LABEL: llvm.func @_mlir_ciface_res_attrs_with_memref_return
 // CHECK-SAME: !llvm.ptr
 // CHECK-NOT: test.returnOne
 func.func private @res_attrs_with_memref_return() -> (memref<f32> {test.returnOne})
 
-// CHECK: llvm.func @res_attrs_with_value_return() -> (f32 {test.returnOne = 1 : i64})
+// CHECK: llvm.func internal @res_attrs_with_value_return() -> (f32 {test.returnOne = 1 : i64})
 // CHECK-LABEL: llvm.func @_mlir_ciface_res_attrs_with_value_return
 // CHECK-SAME: -> (f32 {test.returnOne = 1 : i64})
 func.func private @res_attrs_with_value_return() -> (f32 {test.returnOne = 1})
 
-// CHECK: llvm.func @multiple_return() -> !llvm.struct<{{.*}}>
+// CHECK: llvm.func internal @multiple_return() -> !llvm.struct<{{.*}}>
 // CHECK-LABEL: llvm.func @_mlir_ciface_multiple_return
 // CHECK-NOT: test.returnOne
 // CHECK-NOT: test.returnTwo
 // CHECK-NOT: test.returnThree
 func.func private @multiple_return() -> (memref<f32> {test.returnOne = 1}, f32 {test.returnTwo = 2, test.returnThree = 3})
 
-// CHECK: llvm.func @multiple_return_missing_res_attr() -> !llvm.struct<{{.*}}>
+// CHECK: llvm.func internal @multiple_return_missing_res_attr() -> !llvm.struct<{{.*}}>
 // CHECK-LABEL: llvm.func @_mlir_ciface_multiple_return_missing_res_attr
 // CHECK-NOT: test.returnOne
 // CHECK-NOT: test.returnTwo
 // CHECK-NOT: test.returnThree
 func.func private @multiple_return_missing_res_attr() -> (memref<f32> {test.returnOne = 1}, i64, f32 {test.returnTwo = 2, test.returnThree = 3})
 
-// CHECK: llvm.func @one_arg_attr_no_res_attrs_with_memref_return({{.*}}) -> !llvm.struct{{.*}}
+// CHECK: llvm.func internal @one_arg_attr_no_res_attrs_with_memref_return({{.*}}) -> !llvm.struct{{.*}}
 // CHECK-LABEL: llvm.func @_mlir_ciface_one_arg_attr_no_res_attrs_with_memref_return
 // CHECK-SAME: !llvm.ptr
 // CHECK-SAME: !llvm.ptr
 // CHECK-SAME: {test.argOne = 1 : i64})
 func.func private @one_arg_attr_no_res_attrs_with_memref_return(%arg0: memref<f32> {test.argOne = 1}) -> memref<f32>
 
-// CHECK: llvm.func @one_arg_attr_one_res_attr_with_memref_return({{.*}}) -> (!llvm.struct<{{.*}}> {test.returnOne = 1 : i64})
+// CHECK: llvm.func internal @one_arg_attr_one_res_attr_with_memref_return({{.*}}) -> (!llvm.struct<{{.*}}> {test.returnOne = 1 : i64})
 // CHECK-LABEL: llvm.func @_mlir_ciface_one_arg_attr_one_res_attr_with_memref_return
 // CHECK-SAME: !llvm.ptr
 // CHECK-NOT: test.returnOne
@@ -40,14 +40,14 @@
 // CHECK-SAME: {test.argOne = 1 : i64})
 func.func private @one_arg_attr_one_res_attr_with_memref_return(%arg0: memref<f32> {test.argOne = 1}) -> (memref<f32> {test.returnOne = 1})
 
-// CHECK: llvm.func @one_arg_attr_one_res_attr_with_value_return({{.*}}) -> (f32 {test.returnOne = 1 : i64})
+// CHECK: llvm.func internal @one_arg_attr_one_res_attr_with_value_return({{.*}}) -> (f32 {test.returnOne = 1 : i64})
 // CHECK-LABEL: llvm.func @_mlir_ciface_one_arg_attr_one_res_attr_with_value_return
 // CHECK-SAME: !llvm.ptr
 // CHECK-SAME: {test.argOne = 1 : i64}
 // CHECK-SAME: -> (f32 {test.returnOne = 1 : i64})
 func.func private @one_arg_attr_one_res_attr_with_value_return(%arg0: memref<f32> {test.argOne = 1}) -> (f32 {test.returnOne = 1})
 
-// CHECK: llvm.func @multiple_arg_attr_multiple_res_attr({{.*}}) -> !llvm.struct<{{.*}}>
+// CHECK: llvm.func internal @multiple_arg_attr_multiple_res_attr({{.*}}) -> !llvm.struct<{{.*}}>
 // CHECK-LABEL: llvm.func @_mlir_ciface_multiple_arg_attr_multiple_res_attr
 // CHECK-SAME: !llvm.ptr
 // CHECK-NOT: test.returnOne