diff --git a/changes/3603.bugfix.md b/changes/3603.bugfix.md
new file mode 100644
index 0000000000..37e1da5cb1
--- /dev/null
+++ b/changes/3603.bugfix.md
@@ -0,0 +1 @@
+Correct the target bytes number for auto-chunking when auto-sharding.
\ No newline at end of file
diff --git a/src/zarr/core/chunk_grids.py b/src/zarr/core/chunk_grids.py
index 7ebd68b5b4..2c7945fa64 100644
--- a/src/zarr/core/chunk_grids.py
+++ b/src/zarr/core/chunk_grids.py
@@ -62,6 +62,8 @@ def _guess_chunks(
     tuple[int, ...]
 
     """
+    if min_bytes >= max_bytes:
+        raise ValueError(f"Cannot have more min_bytes ({min_bytes}) than max_bytes ({max_bytes})")
     if isinstance(shape, int):
         shape = (shape,)
 
@@ -264,7 +266,7 @@ def _auto_partition(
     else:
         if chunk_shape == "auto":
             # aim for a 1MiB chunk
-            _chunks_out = _guess_chunks(array_shape, item_size, max_bytes=1024)
+            _chunks_out = _guess_chunks(array_shape, item_size, max_bytes=1048576)
         else:
             _chunks_out = chunk_shape
 
diff --git a/tests/test_array.py b/tests/test_array.py
index 61828be0aa..67be294827 100644
--- a/tests/test_array.py
+++ b/tests/test_array.py
@@ -1019,6 +1019,24 @@ def test_auto_partition_auto_shards(
     assert auto_shards == expected_shards
 
 
+def test_auto_partition_auto_shards_with_auto_chunks_should_be_close_to_1MiB() -> None:
+    """
+    Test that automatically picking a shard size and a chunk size gives roughly 1MiB chunks.
+    """
+    with pytest.warns(
+        ZarrUserWarning,
+        match="Automatic shard shape inference is experimental and may change without notice.",
+    ):
+        with zarr.config.set({"array.target_shard_size_bytes": 10_000_000}):
+            _, chunk_shape = _auto_partition(
+                array_shape=(10_000_000,),
+                chunk_shape="auto",
+                shard_shape="auto",
+                item_size=1,
+            )
+    assert chunk_shape == (625000,)
+
+
 def test_chunks_and_shards() -> None:
     store = StorePath(MemoryStore())
     shape = (100, 100)