diff --git a/cpp/src/arrow/stl_allocator.h b/cpp/src/arrow/stl_allocator.h
index bb52767282ec..62585809c785 100644
--- a/cpp/src/arrow/stl_allocator.h
+++ b/cpp/src/arrow/stl_allocator.h
@@ -19,6 +19,7 @@
 
 #include <algorithm>
 #include <cstddef>
+#include <limits>
 #include <memory>
 #include <string>
 #include <utility>
@@ -72,6 +73,9 @@ class allocator {
   const_pointer address(const_reference r) const noexcept { return std::addressof(r); }
 
   pointer allocate(size_type n, const void* /*hint*/ = NULLPTR) {
+    if (n > size_max() || n > std::numeric_limits<int64_t>::max() / sizeof(T)) {
+      throw BadAlloc(Status::OutOfMemory("Memory allocation size too large"));
+    }
     uint8_t* data;
     Status s = pool_->Allocate(n * sizeof(T), &data);
     if (!s.ok()) throw BadAlloc(std::move(s));
diff --git a/cpp/src/arrow/stl_test.cc b/cpp/src/arrow/stl_test.cc
index ce5adf0c0e26..39916e1fc009 100644
--- a/cpp/src/arrow/stl_test.cc
+++ b/cpp/src/arrow/stl_test.cc
@@ -558,6 +558,20 @@ TEST(allocator, MemoryTracking) {
   ASSERT_EQ(0, pool->bytes_allocated());
 }
 
+TEST(allocator, AllocationSizeOverflow) {
+  allocator<uint64_t> alloc;
+  const size_t first_overflow = std::numeric_limits<size_t>::max() / sizeof(uint64_t) + 1;
+  for (const size_t n : {first_overflow, first_overflow + 1}) {
+    SCOPED_TRACE(n);
+    EXPECT_THROW(
+        {
+          auto* data = alloc.allocate(n);
+          alloc.deallocate(data, n);
+        },
+        std::bad_alloc);
+  }
+}
+
 #if !(defined(ARROW_VALGRIND) || defined(ADDRESS_SANITIZER) || defined(ARROW_JEMALLOC))
 
 TEST(allocator, TestOOM) {