diff --git a/qiskit/qasm3/exporter.py b/qiskit/qasm3/exporter.py
index 561e59a72242..c76e296d6bab 100644
--- a/qiskit/qasm3/exporter.py
+++ b/qiskit/qasm3/exporter.py
@@ -140,9 +140,16 @@ def __init__(
     ):
         """
         Args:
-            includes: the filenames that should be emitted as includes.  These files will be parsed
-                for gates, and any objects dumped from this exporter will use those definitions
-                where possible.
+            includes: the filenames that should be emitted as includes.
+
+                .. note::
+
+                    At present, only the standard-library file ``stdgates.inc`` is properly
+                    understood by the exporter, in the sense that it knows the gates it defines.
+                    You can specify other includes, but you will need to pass the names of the gates
+                    they define in the ``basis_gates`` argument to avoid the exporter outputting a
+                    separate ``gate`` definition.
+
             basis_gates: the basic defined gate set of the backend.
             disable_constants: if ``True``, always emit floating-point constants for numeric
                 parameter values.  If ``False`` (the default), then values close to multiples of
@@ -675,9 +682,9 @@ def build_program(self):
     def build_includes(self):
         """Builds a list of included files."""
         for filename in self.includes:
-            if (definitions := _KNOWN_INCLUDES.get(filename)) is None:
-                raise QASM3ExporterError(f"Unknown OpenQASM 3 include file: '{filename}'")
-            for name, gate in definitions.items():
+            # Note: unknown include files have a corresponding `include` statement generated, but do
+            # not actually define any gates; we rely on the user to pass those in `basis_gates`.
+            for name, gate in _KNOWN_INCLUDES.get(filename, {}).items():
                 self.symbols.register_gate_without_definition(name, gate)
             yield ast.Include(filename)
 
diff --git a/releasenotes/notes/qasm3-includes-ceb56f49b8c190ff.yaml b/releasenotes/notes/qasm3-includes-ceb56f49b8c190ff.yaml
new file mode 100644
index 000000000000..25270fcb6359
--- /dev/null
+++ b/releasenotes/notes/qasm3-includes-ceb56f49b8c190ff.yaml
@@ -0,0 +1,11 @@
+---
+fixes:
+  - |
+    The OpenQASM 3 exporter has restored its behavior of accepting non-standard-library include
+    files in the ``includes`` argument to :func:`.qasm3.dump`, :func:`~.qasm3.dumps`, and
+    :class:`~.qasm3.Exporter`.  These will insert a suitable ``include`` statement into the output
+    as before, and the exporter remains unaware of the intended gates in that include file; you
+    should pass the gates you expect it to define in the ``basis_gates`` argument to the same functions.
+
+    We expect to improve the export mechanism against non-standard include files in a future release
+    of Qiskit.
diff --git a/test/python/qasm3/test_export.py b/test/python/qasm3/test_export.py
index 868846925753..eefc0a2cc53c 100644
--- a/test/python/qasm3/test_export.py
+++ b/test/python/qasm3/test_export.py
@@ -693,6 +693,25 @@ def test_no_include(self):
 """
         self.assertEqual(Exporter(includes=[]).dumps(circuit), expected_qasm)
 
+    def test_include_unknown_file(self):
+        """Test export can target a non-standard include without complaints."""
+        qc = QuantumCircuit(2, 2)
+        qc.h(0)
+        qc.cx(0, 1)
+        qc.measure([0, 1], [0, 1])
+
+        expected = """\
+OPENQASM 3.0;
+include "mygates.inc";
+bit[2] c;
+qubit[2] q;
+h q[0];
+cx q[0], q[1];
+c[0] = measure q[0];
+c[1] = measure q[1];
+"""
+        self.assertEqual(dumps(qc, includes=["mygates.inc"], basis_gates=["h", "cx"]), expected)
+
     def test_teleportation(self):
         """Teleportation with physical qubits"""
         qc = QuantumCircuit(3, 2)