diff --git a/doc/release_notes.rst b/doc/release_notes.rst
index 4c8bb82f..d866d86d 100644
--- a/doc/release_notes.rst
+++ b/doc/release_notes.rst
@@ -94,6 +94,7 @@ Upcoming Version
 * ``sum()`` over a dimension no longer raises when another dimension of the expression has size 0; it returns an expression without terms over the kept coordinates, as summing over the empty dimension itself already did. (https://github.com/PyPSA/linopy/issues/906)
 * A multi-key ``groupby`` now returns its groups sorted by key tuple, like the single-key path. The key combinations were numbered by iterating a ``set``, so the group order was arbitrary and changed between processes with ``PYTHONHASHSEED``.
 * The ``linopy.options`` context manager now restores the values that were active on entry instead of resetting all options to their defaults.
+* Freezing a constraint (``freeze=True``) with a ``MultiIndex`` dimension no longer raises ``TypeError: Must pass list-like as `names```. Building the CSR grid renamed the index to its dimension, which renames the levels of a ``MultiIndex``.
 * ``Model.copy`` (and the ``copy.copy``/``copy.deepcopy`` protocols) no longer downgrades a quadratic objective to a linear one. The objective was rebuilt as a ``LinearExpression`` regardless of its type, so the copy silently solved a different problem. ``linopy.testing.assert_model_equal`` now compares the objective by expression type as well, which it could not do before. (`#903 <https://github.com/PyPSA/linopy/issues/903>`__)
 * ``Model.to_netcdf``/``linopy.read_netcdf`` downgraded a quadratic objective the same way; the expression type is now stored alongside the objective and restored on read. Files written by earlier versions are read as before. (`#903 <https://github.com/PyPSA/linopy/issues/903>`__)
 * ``linopy.read_netcdf`` now restores variables, expressions and constraints in their original insertion order instead of alphabetically, so ``matrices.A`` of a round-tripped model is no longer a row/column permutation of the original. The order is stored in the file; files written by earlier versions still load in sorted order. ``linopy.testing.assert_model_equal`` now also compares container order. (`#934 <https://github.com/PyPSA/linopy/issues/934>`__)
diff --git a/linopy/csr.py b/linopy/csr.py
index 7c27463a..3a5f3f16 100644
--- a/linopy/csr.py
+++ b/linopy/csr.py
@@ -92,7 +92,7 @@ def from_coords(cls, coords: Iterable[pd.Index]) -> Grid:
     def from_dataset(cls, ds: Dataset | DataArray, dims: Iterable[str]) -> Grid:
         """Build from the indexes and auxiliary coordinates ``ds`` carries on ``dims``."""
         dims = tuple(dims)
-        indexes = {d: ds.get_index(d).rename(d) for d in dims}
+        indexes = {d: _named(ds.get_index(d), d) for d in dims}
         return cls(indexes, _aux_coords(ds, set(dims)))
 
     @classmethod
@@ -373,7 +373,7 @@ def from_grouper(
         )
         for d in coord_dims:
             if d != member_dim:
-                indexes[d] = ds.get_index(d).rename(d)
+                indexes[d] = _named(ds.get_index(d), d)
         aux |= _aux_coords(ds, set(coord_dims) - {member_dim})
         grid = Grid({d: indexes[d] for d in grid_dims}, aux)
         if isinstance(source, Dataset):
@@ -837,6 +837,15 @@ def _readonly(values: np.ndarray) -> np.ndarray:
     return values
 
 
+def _named(index: pd.Index, dim: str) -> pd.Index:
+    """``index`` named after ``dim``, keeping the level names of a MultiIndex."""
+    if isinstance(index, pd.MultiIndex):
+        index = index.copy()
+        index.name = dim
+        return index
+    return index.rename(dim)
+
+
 def _aux_coords(ds: Dataset | DataArray, dims: set[str]) -> AuxCoords:
     """Scalar and one-dimensional auxiliary coordinates of ``ds`` lying on ``dims``."""
     aux: AuxCoords = {}
diff --git a/test/test_io.py b/test/test_io.py
index dabee6f5..b3566434 100644
--- a/test/test_io.py
+++ b/test/test_io.py
@@ -399,6 +399,24 @@ def test_model_to_netcdf_with_multiindex(
     assert_model_equal(m, p)
 
 
+def test_model_to_netcdf_with_multiindex_frozen_constraint(
+    model_with_multiindex: Model, tmp_path: Path
+) -> None:
+    from linopy.constraints import CSRConstraint
+
+    m = model_with_multiindex
+    x, y = m.variables["x-var"], m.variables["y-var"]
+    con = m.add_constraints(x + y, LESS_EQUAL, 10, name="frozen", freeze=True)
+    assert isinstance(con, CSRConstraint)
+
+    fn = tmp_path / "test.nc"
+    m.to_netcdf(fn)
+    p = read_netcdf(fn)
+
+    assert isinstance(p.constraints["frozen"], CSRConstraint)
+    assert_model_equal(m, p)
+
+
 # Regression for https://github.com/PyPSA/linopy/issues/525.
 def test_model_to_netcdf_with_multiindex_scipy_engine(
     model_with_multiindex: Model, tmp_path: Path