diff --git a/r/src/compute-exec.cpp b/r/src/compute-exec.cpp
index 6647c35d49d76..8b20d581062d7 100644
--- a/r/src/compute-exec.cpp
+++ b/r/src/compute-exec.cpp
@@ -88,42 +88,47 @@ class ExecPlanReader : public arrow::RecordBatchReader {
       *batch_out = batch_result.ValueUnsafe();
     } else {
       batch_out->reset();
+      StopProducing();
     }
 
     return arrow::Status::OK();
   }
 
   arrow::Status Close() {
-    plan_.reset();
-    status_ = 2;
+    StopProducing();
     return arrow::Status::OK();
   }
 
   const std::shared_ptr<arrow::compute::ExecPlan>& Plan() { return plan_; }
 
+  ~ExecPlanReader() { StopProducing(); }
+
  private:
   std::shared_ptr<arrow::Schema> schema_;
   std::shared_ptr<arrow::compute::ExecPlan> plan_;
   arrow::AsyncGenerator<arrow::util::optional<compute::ExecBatch>> sink_gen_;
-  std::shared_ptr<void> stop_producing_;
   int status_;
 
   arrow::Status StartProducing() {
     ARROW_RETURN_NOT_OK(plan_->StartProducing());
     status_ = 1;
+    return arrow::Status::OK();
+  }
 
-    // If the generator is destroyed before being completely drained, inform plan
-    const std::shared_ptr<arrow::compute::ExecPlan> plan(plan_);
-    stop_producing_ = {nullptr, [plan](...) {
-                         bool not_finished_yet = plan->finished().TryAddCallback(
-                             [&plan] { return [plan](const arrow::Status&) {}; });
+  void StopProducing() {
+    if (status_ == 1) {
+      std::shared_ptr<arrow::compute::ExecPlan> plan(plan_);
+      bool not_finished_yet = plan_->finished().TryAddCallback(
+          [&plan] { return [plan](const arrow::Status&) {}; });
 
-                         if (not_finished_yet) {
-                           plan->StopProducing();
-                         }
-                       }};
+      if (not_finished_yet) {
+        plan_->StopProducing();
+      }
 
-    return arrow::Status::OK();
+      status_ = 2;
+      plan_.reset();
+      sink_gen_ = arrow::MakeEmptyGenerator<arrow::util::optional<compute::ExecBatch>>();
+    }
   }
 };