diff --git a/haystack/components/preprocessors/csv_document_splitter.py b/haystack/components/preprocessors/csv_document_splitter.py
index ea1dfa78c5..3850e4ba82 100644
--- a/haystack/components/preprocessors/csv_document_splitter.py
+++ b/haystack/components/preprocessors/csv_document_splitter.py
@@ -6,9 +6,10 @@
 from io import StringIO
 from typing import Any, Literal, get_args
 
-from haystack import Document, component, logging
 from haystack.lazy_imports import LazyImport
 
+from haystack import Document, component, logging
+
 with LazyImport("Run 'pip install pandas'") as pandas_import:
     import pandas as pd
 
@@ -145,8 +146,15 @@ def run(self, documents: list[Document]) -> dict[str, list[Document]]:
                 )
                 continue
 
-            # Sort split_dfs first by row index, then by column index
-            split_dfs.sort(key=lambda dataframe: (dataframe.index[0], dataframe.columns[0]))
+            # Columns are only positional when ``header=None``. A caller passing
+            # ``read_csv_kwargs={"header": 0}`` gets the first row as string labels,
+            # so ``int(label)`` failed for every sub-table and sorting on the label
+            # ordered the sub-tables alphabetically. Map labels back to their
+            # position in the original frame instead.
+            column_positions = {label: position for position, label in enumerate(df.columns)}
+
+            # Sort split_dfs first by row index, then by column position
+            split_dfs.sort(key=lambda dataframe: (dataframe.index[0], column_positions[dataframe.columns[0]]))
 
             for split_id, split_df in enumerate(split_dfs):
                 split_documents.append(
@@ -156,7 +164,7 @@ def run(self, documents: list[Document]) -> dict[str, list[Document]]:
                             **deepcopy(document.meta),
                             "source_id": document.id,
                             "row_idx_start": int(split_df.index[0]),
-                            "col_idx_start": int(split_df.columns[0]),
+                            "col_idx_start": column_positions[split_df.columns[0]],
                             "split_id": split_id,
                         },
                     )
diff --git a/releasenotes/notes/csv-splitter-header-kwargs-fc8ce7f31997395f.yaml b/releasenotes/notes/csv-splitter-header-kwargs-fc8ce7f31997395f.yaml
new file mode 100644
index 0000000000..5045e559c4
--- /dev/null
+++ b/releasenotes/notes/csv-splitter-header-kwargs-fc8ce7f31997395f.yaml
@@ -0,0 +1,9 @@
+---
+fixes:
+  - |
+    ``CSVDocumentSplitter`` now reports the column position of each sub-table and orders
+    sub-tables by column position instead of by column label. Passing
+    ``read_csv_kwargs={"header": 0}`` used to raise ``ValueError: invalid literal for int()
+    with base 10`` for every sub-table, because ``header=None`` was the only case in which
+    the labels were positional; with a caller-supplied header the labels are strings, and
+    sorting on them reordered the sub-tables alphabetically.
diff --git a/test/components/preprocessors/test_csv_document_splitter_header_kwargs.py b/test/components/preprocessors/test_csv_document_splitter_header_kwargs.py
new file mode 100644
index 0000000000..0e27ff35d1
--- /dev/null
+++ b/test/components/preprocessors/test_csv_document_splitter_header_kwargs.py
@@ -0,0 +1,28 @@
+"""read_csv_kwargs that sets a header must not break CSV splitting."""
+
+from haystack import Document
+from haystack.components.preprocessors.csv_document_splitter import CSVDocumentSplitter
+
+ROWS = "name,score\nAda,9\n\nBob,8"
+COLUMNS = "z,_,a\n1,,2\n3,,4\n"
+
+
+def test_default_header_none_keeps_positional_columns():
+    splitter = CSVDocumentSplitter(row_split_threshold=1, column_split_threshold=None)
+    result = splitter.run([Document(content=ROWS)])
+    assert [(d.meta["row_idx_start"], d.meta["col_idx_start"]) for d in result["documents"]] == [(0, 0), (3, 0)]
+
+
+def test_read_csv_kwargs_header_reports_column_positions():
+    """With a caller-supplied header the columns are labels, not positions."""
+    splitter = CSVDocumentSplitter(row_split_threshold=1, column_split_threshold=None, read_csv_kwargs={"header": 0})
+    result = splitter.run([Document(content=ROWS)])
+    assert [(d.meta["row_idx_start"], d.meta["col_idx_start"]) for d in result["documents"]] == [(0, 0), (2, 0)]
+
+
+def test_header_labels_do_not_reorder_sub_tables():
+    """Sub-tables keep the original column order, not the alphabetical one."""
+    splitter = CSVDocumentSplitter(row_split_threshold=None, column_split_threshold=1, read_csv_kwargs={"header": 0})
+    result = splitter.run([Document(content=COLUMNS)])
+    assert [(d.meta["col_idx_start"], d.meta["split_id"]) for d in result["documents"]] == [(0, 0), (2, 1)]
+    assert [d.content.strip().replace("\n", "/") for d in result["documents"]] == ["1/3", "2/4"]