diff --git a/mlir/lib/Dialect/Linalg/Transforms/FusionOnTensors.cpp b/mlir/lib/Dialect/Linalg/Transforms/FusionOnTensors.cpp
--- a/mlir/lib/Dialect/Linalg/Transforms/FusionOnTensors.cpp
+++ b/mlir/lib/Dialect/Linalg/Transforms/FusionOnTensors.cpp
@@ -1099,6 +1099,12 @@
           linalgOp.indexing_maps().getAsValueRange<AffineMapAttr>());
       fusedIndexMaps.erase(std::next(fusedIndexMaps.begin(), operand.index()));
 
+      // Check if the operation shapes to loops map is computable.
+      if (!inversePermutation(concatAffineMaps(fusedIndexMaps))) {
+        return rewriter.notifyMatchFailure(
+            linalgOp, "fused op loop bound computation failed");
+      }
+
       // The operands list is same as the linalgOp with the argument for
       // constant index dropped.
       SmallVector<Value, 4> fusedOperands(linalgOp.getInputs());
diff --git a/mlir/test/Dialect/Linalg/fusion-tensor.mlir b/mlir/test/Dialect/Linalg/fusion-tensor.mlir
--- a/mlir/test/Dialect/Linalg/fusion-tensor.mlir
+++ b/mlir/test/Dialect/Linalg/fusion-tensor.mlir
@@ -652,3 +652,26 @@
   // CHECK-NEXT:   return %[[R]] : tensor<1x8xi32>
   return %1 : tensor<1x8xi32>
 }
+
+// -----
+
+// CHECK-LABEL: func @no_fuse_constant_with_reduction
+func @no_fuse_constant_with_reduction() -> tensor<3xf32>
+{
+  //      CHECK: %[[CONST:.+]] = constant {{.+}} : tensor<3x2xf32>
+  //      CHECK: %[[RESULT:.+]] = linalg.generic
+  // CHECK-SAME:   ins(%[[CONST]] : tensor<3x2xf32>)
+  //      CHECK: return %[[RESULT]]
+  %three = constant dense<3.0> : tensor<3x2xf32>
+  %init = linalg.init_tensor [3] : tensor<3xf32>
+  %result = linalg.generic {
+      indexing_maps = [affine_map<(d0, d1) -> (d0, d1)>,
+                       affine_map<(d0, d1) -> (d0)>],
+      iterator_types = ["parallel", "reduction"]}
+     ins(%three : tensor<3x2xf32>) outs(%init : tensor<3xf32>) {
+     ^bb0(%arg0 : f32, %arg1 : f32):
+        %0 = addf %arg0, %arg1 : f32
+        linalg.yield %0 : f32
+  } -> tensor<3xf32>
+  return %result : tensor<3xf32>
+}