diff --git a/python/pyarrow/includes/libarrow.pxd b/python/pyarrow/includes/libarrow.pxd
index e57c6d0d92d..efc9602a3a8 100644
--- a/python/pyarrow/includes/libarrow.pxd
+++ b/python/pyarrow/includes/libarrow.pxd
@@ -2011,6 +2011,8 @@ cdef extern from "arrow/ipc/api.h" namespace "arrow::ipc" nogil:
 
         CResult[CRecordBatchWithMetadata] ReadRecordBatchWithCustomMetadata(int i)
 
+        CResult[int64_t] CountRows()
+
         CIpcReadStats stats()
 
         shared_ptr[const CKeyValueMetadata] metadata()
diff --git a/python/pyarrow/ipc.pxi b/python/pyarrow/ipc.pxi
index 6477579af21..991505a2b7f 100644
--- a/python/pyarrow/ipc.pxi
+++ b/python/pyarrow/ipc.pxi
@@ -1192,6 +1192,39 @@ cdef class _RecordBatchFileReader(_Weakrefable):
         """
         return self.reader.get().num_record_batches()
 
+    def count_rows(self):
+        """
+        The total number of rows in the IPC file.
+
+        This reads the metadata of each record batch in the file, without
+        deserializing the record batches themselves.
+
+        Returns
+        -------
+        count : int
+
+        Examples
+        --------
+        >>> import pyarrow as pa
+        >>> schema = pa.schema([('a', pa.int64())])
+        >>> sink = pa.BufferOutputStream()
+        >>> with pa.ipc.new_file(sink, schema) as writer:
+        ...     for i in range(3):
+        ...         writer.write_batch(pa.record_batch([[1, 2]], schema=schema))
+        >>> with pa.ipc.open_file(sink.getvalue()) as reader:
+        ...     reader.count_rows()
+        6
+        """
+        cdef int64_t nrows
+
+        if not self.reader:
+            raise ValueError("Operation on closed reader")
+
+        with nogil:
+            nrows = GetResultValue(self.reader.get().CountRows())
+
+        return nrows
+
     def get_batch(self, int i):
         """
         Read the record batch with the given index.
diff --git a/python/pyarrow/tests/test_ipc.py b/python/pyarrow/tests/test_ipc.py
index 6813ed77723..121617371c9 100644
--- a/python/pyarrow/tests/test_ipc.py
+++ b/python/pyarrow/tests/test_ipc.py
@@ -189,6 +189,30 @@ def test_file_read_all(sink_factory):
     assert result.equals(expected)
 
 
+def test_file_count_rows(file_fixture):
+    batches = file_fixture.write_batches()
+    file_contents = pa.BufferReader(file_fixture.get_source())
+
+    reader = pa.ipc.open_file(file_contents)
+
+    expected = sum(batch.num_rows for batch in batches)
+    assert reader.count_rows() == expected
+    # counting the rows does not consume the reader
+    assert reader.read_all().num_rows == expected
+    assert reader.count_rows() == expected
+
+
+def test_file_count_rows_no_batches():
+    schema = pa.schema([('a', pa.int64())])
+    sink = pa.BufferOutputStream()
+    with pa.ipc.new_file(sink, schema):
+        pass
+
+    reader = pa.ipc.open_file(sink.getvalue())
+    assert reader.num_record_batches == 0
+    assert reader.count_rows() == 0
+
+
 def test_open_file_from_buffer(file_fixture):
     # ARROW-2859; APIs accept the buffer protocol
     file_fixture.write_batches()