diff --git a/cpp/src/plasma/eviction_policy.cc b/cpp/src/plasma/eviction_policy.cc
index e5beb5a579e..44082c810a6 100644
--- a/cpp/src/plasma/eviction_policy.cc
+++ b/cpp/src/plasma/eviction_policy.cc
@@ -73,6 +73,10 @@ void EvictionPolicy::ObjectCreated(const ObjectID& object_id) {
   ARROW_CHECK(memory_used_ <= store_info_->memory_capacity);
 }
 
+bool EvictionPolicy::AbleToAdd(int64_t need_size) {
+  return memory_used_ + need_size <= store_info_->memory_capacity;
+}
+
 bool EvictionPolicy::RequireSpace(int64_t size, std::vector<ObjectID>* objects_to_evict) {
   // Check if there is enough space to create the object.
   int64_t required_space = memory_used_ + size - store_info_->memory_capacity;
diff --git a/cpp/src/plasma/eviction_policy.h b/cpp/src/plasma/eviction_policy.h
index bbd3fc43203..6a432c13450 100644
--- a/cpp/src/plasma/eviction_policy.h
+++ b/cpp/src/plasma/eviction_policy.h
@@ -125,6 +125,11 @@ class EvictionPolicy {
   /// @param object_id The ID of the object that is now being used.
   void RemoveObject(const ObjectID& object_id);
 
+  /// To check whether we can add an object of a specific size.
+  ///
+  /// @param size The object size to check.
+  bool AbleToAdd(int64_t size);
+
  private:
   /// The amount of memory (in bytes) currently being used.
   int64_t memory_used_;
diff --git a/cpp/src/plasma/store.cc b/cpp/src/plasma/store.cc
index 58f8d0193ce..0e21b739740 100644
--- a/cpp/src/plasma/store.cc
+++ b/cpp/src/plasma/store.cc
@@ -175,9 +175,11 @@ PlasmaError PlasmaStore::CreateObject(const ObjectID& object_id, int64_t data_si
     // it is not guaranteed that the corresponding pointer in the client will be
     // 64-byte aligned, but in practice it often will be.
     if (device_num == 0) {
-      pointer =
-          reinterpret_cast<uint8_t*>(dlmemalign(kBlockSize, data_size + metadata_size));
       if (pointer == nullptr) {
+        pointer =
+            reinterpret_cast<uint8_t*>(dlmemalign(kBlockSize, data_size + metadata_size));
+      }
+      if (pointer == nullptr || !eviction_policy_.AbleToAdd(data_size + metadata_size)) {
         // Tell the eviction policy how much space we need to create this object.
         std::vector<ObjectID> objects_to_evict;
         bool success =
diff --git a/cpp/src/plasma/test/client_tests.cc b/cpp/src/plasma/test/client_tests.cc
index 1ad60396af9..8f4ccee0dcc 100644
--- a/cpp/src/plasma/test/client_tests.cc
+++ b/cpp/src/plasma/test/client_tests.cc
@@ -47,7 +47,8 @@ void AssertObjectBufferEqual(const ObjectBuffer& object_buffer,
   arrow::AssertBufferEqual(*object_buffer.data, data);
 }
 
-class TestPlasmaStore : public ::testing::Test {
+template <unsigned int M>
+class TestPlasmaStoreBase : public ::testing::Test {
  public:
   // TODO(pcm): At the moment, stdout of the test gets mixed up with
   // stdout of the object store. Consider changing that.
@@ -59,9 +60,10 @@ class TestPlasmaStore : public ::testing::Test {
 
     std::string plasma_directory =
         test_executable.substr(0, test_executable.find_last_of("/"));
-    std::string plasma_command = plasma_directory +
-                                 "/plasma_store_server -m 1000000000 -s " +
-                                 store_socket_name_ + " 1> /dev/null 2> /dev/null &";
+    std::ostringstream ostream;
+    ostream << plasma_directory << "/plasma_store_server -m " << M << " -s "
+            << store_socket_name_ + " 1> /dev/null 2> /dev/null &";
+    std::string plasma_command = ostream.str();
     system(plasma_command.c_str());
     ARROW_CHECK_OK(client_.Connect(store_socket_name_, ""));
     ARROW_CHECK_OK(client2_.Connect(store_socket_name_, ""));
@@ -101,6 +103,8 @@ class TestPlasmaStore : public ::testing::Test {
   std::string store_socket_name_;
 };
 
+using TestPlasmaStore = TestPlasmaStoreBase<1000000000>;
+
 TEST_F(TestPlasmaStore, NewSubscriberTest) {
   PlasmaClient local_client, local_client2;
 
@@ -487,6 +491,33 @@ TEST_F(TestPlasmaStore, ManyObjectTest) {
   }
 }
 
+using TestSmallMemoryPlasmaStore = TestPlasmaStoreBase<1000>;
+
+TEST_F(TestSmallMemoryPlasmaStore, SmallMemoryTest) {
+  // Create many objects on the first client. Seal one third, abort one third,
+  // and leave the last third unsealed.
+  std::vector<ObjectID> object_ids;
+  for (int i = 0; i < 10; i++) {
+    ObjectID object_id = random_object_id();
+    object_ids.push_back(object_id);
+
+    // Test for object non-existence on the first client.
+    bool has_object;
+    ARROW_CHECK_OK(client_.Contains(object_id, &has_object));
+    ASSERT_FALSE(has_object);
+
+    // Test for the object being in local Plasma store.
+    // First create and seal object on the first client.
+    int64_t data_size = 100;
+    uint8_t metadata[] = {5};
+    int64_t metadata_size = sizeof(metadata);
+    std::shared_ptr<Buffer> data;
+    ARROW_CHECK_OK(client_.Create(object_id, data_size, metadata, metadata_size, &data));
+    ARROW_CHECK_OK(client_.Seal(object_id));
+    ARROW_CHECK_OK(client_.Release(object_id));
+  }
+}
+
 #ifdef PLASMA_GPU
 using arrow::gpu::CudaBuffer;
 using arrow::gpu::CudaBufferReader;