diff --git a/csrc/quantization/fp8/common.cu b/csrc/quantization/fp8/common.cu
index 56e3a3f43446a..090f95d1bda71 100644
--- a/csrc/quantization/fp8/common.cu
+++ b/csrc/quantization/fp8/common.cu
@@ -103,11 +103,11 @@ __device__ float thread_max_vec(scalar_t const* __restrict__ input,
   vec4_t<scalar_t> const* vectorized_in =
       reinterpret_cast<vec4_t<scalar_t> const*>(input);
 
-  int const num_vec_elems = num_elems >> 2;
+  int64_t const num_vec_elems = num_elems >> 2;
   float absmax_val = 0.0f;
 
 #pragma unroll 4
-  for (int i = tid; i < num_vec_elems; i += step) {
+  for (int64_t i = tid; i < num_vec_elems; i += step) {
     vec4_t<scalar_t> in_vec = vectorized_in[i];
     absmax_val = max(absmax_val, fabs(in_vec.x));
     absmax_val = max(absmax_val, fabs(in_vec.y));
@@ -116,7 +116,7 @@ __device__ float thread_max_vec(scalar_t const* __restrict__ input,
   }
 
   // Handle the remaining elements if num_elems is not divisible by 4
-  for (int i = num_vec_elems * 4 + tid; i < num_elems; i += step) {
+  for (int64_t i = num_vec_elems * 4 + tid; i < num_elems; i += step) {
     absmax_val = max(absmax_val, fabs(input[i]));
   }
 
@@ -134,10 +134,10 @@ __device__ void scaled_fp8_conversion_vec(c10::Float8_e4m3fn* __restrict__ out,
       reinterpret_cast<vec4_t<scalar_t> const*>(input);
   float8x4_t* vectorized_out = reinterpret_cast<float8x4_t*>(out);
 
-  int const num_vec_elems = num_elems >> 2;
+  int64_t const num_vec_elems = num_elems >> 2;
 
 #pragma unroll 4
-  for (int i = tid; i < num_vec_elems; i += step) {
+  for (int64_t i = tid; i < num_vec_elems; i += step) {
     vec4_t<scalar_t> in_vec = vectorized_in[i];
     float8x4_t out_vec;
 
@@ -153,7 +153,7 @@ __device__ void scaled_fp8_conversion_vec(c10::Float8_e4m3fn* __restrict__ out,
   }
 
   // Handle the remaining elements if num_elems is not divisible by 4
-  for (int i = num_vec_elems * 4 + tid; i < num_elems; i += step) {
+  for (int64_t i = num_vec_elems * 4 + tid; i < num_elems; i += step) {
     out[i] = scaled_fp8_conversion<is_scale_inverted>(
         static_cast<float>(input[i]), scale);
   }
diff --git a/tests/kernels/test_fp8_quant.py b/tests/kernels/test_fp8_quant.py
index bf1a8df649972..61ff54db560da 100644
--- a/tests/kernels/test_fp8_quant.py
+++ b/tests/kernels/test_fp8_quant.py
@@ -60,3 +60,28 @@ def test_dynamic_per_tensor_fp8_quant(num_tokens: int, hidden_size: int,
     assert torch.allclose(ref_scale, ops_scale)
     assert torch.allclose(ref_out.to(dtype=torch.float32),
                           ops_out.to(dtype=torch.float32))
+
+
+# Regression test for a case with large activations where an int32 index cannot
+# represent the number of elements.
+@torch.inference_mode()
+@pytest.mark.parametrize("seed", SEEDS)
+def test_fp8_quant_large(seed: int) -> None:
+    torch.random.manual_seed(seed)
+    torch.cuda.manual_seed(seed)
+
+    num_tokens = 1024000  # Mistral-Nemo's max_position_embeddings
+    hidden_size = 1152  # Smallest hidden_size to reproduce the error
+    dtype = torch.bfloat16
+
+    x = torch.rand(num_tokens, hidden_size, dtype=dtype, device="cuda")
+    ref_out, scale = ref_dynamic_per_tensor_fp8_quant(x)
+    ops_out, _ = ops.scaled_fp8_quant(x, scale)
+
+    # Minimize memory footprint in this test by freeing x and upconverting
+    # the outputs in place. (torch.allclose does not support fp8)
+    del x
+    ref_out = ref_out.to(dtype=dtype)
+    ops_out = ops_out.to(dtype=dtype)
+
+    assert torch.allclose(ref_out, ops_out)