diff --git a/cpp/src/arrow/acero/aggregate_node_test.cc b/cpp/src/arrow/acero/aggregate_node_test.cc
index d398fb24b73d5..c623271db9fb4 100644
--- a/cpp/src/arrow/acero/aggregate_node_test.cc
+++ b/cpp/src/arrow/acero/aggregate_node_test.cc
@@ -210,5 +210,57 @@ TEST(GroupByNode, NoSkipNulls) {
   AssertExecBatchesEqualIgnoringOrder(out_schema, {expected_batch}, out_batches.batches);
 }
 
+TEST(ScalarAggregateNode, AnyAll) {
+  // GH-43768: boolean_any and boolean_all with constant input should work well
+  // when min_count != 0.
+  std::shared_ptr<Schema> in_schema = schema({field("not_used", int32())});
+  std::shared_ptr<Schema> out_schema = schema({field("agg_out", boolean())});
+  struct AnyAllCase {
+    std::string batches_json;
+    Expression literal;
+    std::string expected_json;
+    bool skip_nulls = false;
+    uint32_t min_count = 2;
+  };
+  std::vector<AnyAllCase> cases{
+      {"[[42], [42], [42], [42]]", literal(true), "[[true]]"},
+      {"[[42], [42], [42], [42]]", literal(false), "[[false]]"},
+      {"[[42], [42], [42], [42]]", literal(BooleanScalar{}), "[[null]]"},
+      {"[[42]]", literal(true), "[[null]]"},
+      {"[[42], [42], [42]]", literal(true), "[[true]]"},
+      {"[[42], [42], [42]]", literal(true), "[[null]]", /*skip_nulls=*/false,
+       /*min_count=*/4},
+      {"[[42], [42], [42], [42]]", literal(BooleanScalar{}), "[[null]]",
+       /*skip_nulls=*/true},
+  };
+  for (const AnyAllCase& any_all_case : cases) {
+    for (auto func_name : {"any", "all"}) {
+      std::vector<ExecBatch> batches{
+          ExecBatchFromJSON({int32()}, any_all_case.batches_json)};
+      std::vector<Aggregate> aggregates = {
+          Aggregate(func_name,
+                    std::make_shared<compute::ScalarAggregateOptions>(
+                        /*skip_nulls=*/any_all_case.skip_nulls,
+                        /*min_count=*/any_all_case.min_count),
+                    FieldRef("literal"))};
+
+      // And a projection to make the input including a Scalar Boolean
+      Declaration plan = Declaration::Sequence(
+          {{"exec_batch_source", ExecBatchSourceNodeOptions(in_schema, batches)},
+           {"project", ProjectNodeOptions({any_all_case.literal}, {"literal"})},
+           {"aggregate", AggregateNodeOptions(aggregates)}});
+
+      ASSERT_OK_AND_ASSIGN(BatchesWithCommonSchema out_batches,
+                           DeclarationToExecBatches(plan));
+
+      ExecBatch expected_batch =
+          ExecBatchFromJSON({boolean()}, any_all_case.expected_json);
+
+      AssertExecBatchesEqualIgnoringOrder(out_schema, {expected_batch},
+                                          out_batches.batches);
+    }
+  }
+}
+
 }  // namespace acero
 }  // namespace arrow
diff --git a/cpp/src/arrow/compute/kernels/aggregate_basic.cc b/cpp/src/arrow/compute/kernels/aggregate_basic.cc
index 1fbcd6a249093..c5e0e6fd6e977 100644
--- a/cpp/src/arrow/compute/kernels/aggregate_basic.cc
+++ b/cpp/src/arrow/compute/kernels/aggregate_basic.cc
@@ -532,13 +532,13 @@ struct BooleanAnyImpl : public ScalarAggregator {
     }
     if (batch[0].is_scalar()) {
       const Scalar& scalar = *batch[0].scalar;
-      this->has_nulls = !scalar.is_valid;
-      this->any = scalar.is_valid && checked_cast<const BooleanScalar&>(scalar).value;
-      this->count += scalar.is_valid;
+      this->has_nulls |= !scalar.is_valid;
+      this->any |= scalar.is_valid && checked_cast<const BooleanScalar&>(scalar).value;
+      this->count += scalar.is_valid * batch.length;
       return Status::OK();
     }
     const ArraySpan& data = batch[0].array;
-    this->has_nulls = data.GetNullCount() > 0;
+    this->has_nulls |= data.GetNullCount() > 0;
     this->count += data.length - data.GetNullCount();
     arrow::internal::OptionalBinaryBitBlockCounter counter(
         data.buffers[0].data, data.offset, data.buffers[1].data, data.offset,
@@ -603,13 +603,13 @@ struct BooleanAllImpl : public ScalarAggregator {
     }
     if (batch[0].is_scalar()) {
       const Scalar& scalar = *batch[0].scalar;
-      this->has_nulls = !scalar.is_valid;
-      this->count += scalar.is_valid;
-      this->all = !scalar.is_valid || checked_cast<const BooleanScalar&>(scalar).value;
+      this->has_nulls |= !scalar.is_valid;
+      this->count += scalar.is_valid * batch.length;
+      this->all &= !scalar.is_valid || checked_cast<const BooleanScalar&>(scalar).value;
       return Status::OK();
     }
     const ArraySpan& data = batch[0].array;
-    this->has_nulls = data.GetNullCount() > 0;
+    this->has_nulls |= data.GetNullCount() > 0;
     this->count += data.length - data.GetNullCount();
     arrow::internal::OptionalBinaryBitBlockCounter counter(
         data.buffers[1].data, data.offset, data.buffers[0].data, data.offset,