diff --git a/src/scanpy/preprocessing/_pca.py b/src/scanpy/preprocessing/_pca.py
index 5b5706c123..3a43a3bfc4 100644
--- a/src/scanpy/preprocessing/_pca.py
+++ b/src/scanpy/preprocessing/_pca.py
@@ -263,7 +263,10 @@ def pca(
 
         for chunk, _, _ in adata_comp.chunked_X(chunk_size):
             chunk = chunk.toarray() if issparse(chunk) else chunk
-            pca_.partial_fit(chunk)
+            if n_comps <= chunk.shape[0]:
+                pca_.partial_fit(chunk)
+            else:
+                continue
 
         for chunk, start, end in adata_comp.chunked_X(chunk_size):
             chunk = chunk.toarray() if issparse(chunk) else chunk