diff --git a/mlir/lib/Dialect/Linalg/IR/LinalgOps.cpp b/mlir/lib/Dialect/Linalg/IR/LinalgOps.cpp
--- a/mlir/lib/Dialect/Linalg/IR/LinalgOps.cpp
+++ b/mlir/lib/Dialect/Linalg/IR/LinalgOps.cpp
@@ -995,6 +995,8 @@
     return op.emitOpError("expects memref elemental types to match");
   if (oType.getRank() != iType.getRank() || oType.getRank() != fType.getRank())
     return op.emitOpError("expects memref ranks to match");
+  if (oType.getRank() <= 2)
+    return op.emitError("expects memref ranks to be greater than 2");
   if (auto strides = op.strides()) {
     if (failed(
             verifyStrideOrDilation(op, strides->getValue(), /*isStride=*/true)))
diff --git a/mlir/test/Dialect/Linalg/invalid.mlir b/mlir/test/Dialect/Linalg/invalid.mlir
--- a/mlir/test/Dialect/Linalg/invalid.mlir
+++ b/mlir/test/Dialect/Linalg/invalid.mlir
@@ -428,6 +428,13 @@
 
 // -----
 
+func @conv_rank_limit(%arg0: memref<?xf32>, %arg1: memref<?xf32>, %arg2: memref<?xf32>) {
+  // expected-error @+1 {{expects memref ranks to be greater than 2}}
+  linalg.conv(%arg0, %arg1, %arg2) : memref<?xf32>, memref<?xf32>, memref<?xf32>
+}
+
+// -----
+
 // expected-error @+1 {{unknown Linalg type}}
 !invalid_type = type !linalg.unknown