diff --git a/src/cairo-gstate.c b/src/cairo-gstate.c
index b1fc6b34d..2867243f4 100644
--- a/src/cairo-gstate.c
+++ b/src/cairo-gstate.c
@@ -1289,6 +1289,9 @@ cairo_status_t
 _cairo_gstate_set_font_matrix (cairo_gstate_t	    *gstate,
 			       const cairo_matrix_t *matrix)
 {
+    if (! _cairo_matrix_is_invertible (matrix))
+	return _cairo_error (CAIRO_STATUS_INVALID_MATRIX);
+
     _cairo_gstate_unset_scaled_font (gstate);
 
     gstate->font_matrix = *matrix;
diff --git a/src/cairo-matrix.c b/src/cairo-matrix.c
index cf31c5d4d..00c2d4866 100644
--- a/src/cairo-matrix.c
+++ b/src/cairo-matrix.c
@@ -486,6 +486,16 @@ cairo_matrix_invert (cairo_matrix_t *matrix)
 }
 slim_hidden_def(cairo_matrix_invert);
 
+cairo_bool_t
+_cairo_matrix_is_invertible (const cairo_matrix_t *matrix)
+{
+    double det;
+
+    _cairo_matrix_compute_determinant (matrix, &det);
+
+    return det != 0. && det * det > 0.;
+}
+
 void
 _cairo_matrix_compute_determinant (const cairo_matrix_t *matrix,
 				   double		*det)
diff --git a/src/cairo-scaled-font.c b/src/cairo-scaled-font.c
index 2da991204..e90591746 100644
--- a/src/cairo-scaled-font.c
+++ b/src/cairo-scaled-font.c
@@ -603,6 +603,9 @@ cairo_scaled_font_create (cairo_font_face_t          *font_face,
     if (cairo_font_options_status ((cairo_font_options_t *) options))
 	return (cairo_scaled_font_t *)&_cairo_scaled_font_nil;
 
+    if (! _cairo_matrix_is_invertible (font_matrix))
+	return (cairo_scaled_font_t *)&_cairo_scaled_font_nil;
+
     font_map = _cairo_scaled_font_map_lock ();
     if (font_map == NULL)
 	return (cairo_scaled_font_t *)&_cairo_scaled_font_nil;
diff --git a/src/cairoint.h b/src/cairoint.h
index 80915d770..c5cdf1a5d 100644
--- a/src/cairoint.h
+++ b/src/cairoint.h
@@ -2104,6 +2104,9 @@ _cairo_matrix_transform_bounding_box (const cairo_matrix_t *matrix,
 				      double *x2, double *y2,
 				      cairo_bool_t *is_tight);
 
+cairo_private cairo_bool_t
+_cairo_matrix_is_invertible (const cairo_matrix_t *matrix);
+
 cairo_private void
 _cairo_matrix_compute_determinant (const cairo_matrix_t *matrix, double *det);