diff --git a/qiskit/visualization/bloch.py b/qiskit/visualization/bloch.py
index 97f1c28af148..ac5dd8c3e720 100644
--- a/qiskit/visualization/bloch.py
+++ b/qiskit/visualization/bloch.py
@@ -81,10 +81,12 @@ def __init__(self, xs, ys, zs, zdir="z", **kwargs):
         # pylint: disable=super-init-not-called
         FancyArrowPatch.__init__(self, (0, 0), (0, 0), **kwargs)
         self.set_3d_properties(tuple(zip(xs, ys)), zs, zdir)
+        self._path2d = None
 
     def draw(self, renderer):
         xs3d, ys3d, zs3d = zip(*self._segment3d)
         x_s, y_s, _ = proj3d.proj_transform(xs3d, ys3d, zs3d, self.axes.M)
+        self._path2d = matplotlib.path.Path(np.column_stack([x_s, y_s]))
         self.set_positions((x_s[0], y_s[0]), (x_s[1], y_s[1]))
         FancyArrowPatch.draw(self, renderer)
 
diff --git a/releasenotes/notes/fix-path2d-mpl3.4-b1af3a23b408d30a.yaml b/releasenotes/notes/fix-path2d-mpl3.4-b1af3a23b408d30a.yaml
new file mode 100644
index 000000000000..730d6c7cc0f9
--- /dev/null
+++ b/releasenotes/notes/fix-path2d-mpl3.4-b1af3a23b408d30a.yaml
@@ -0,0 +1,14 @@
+---
+fixes:
+  - |
+    Fixed an issue where plotting Bloch spheres could cause an ``AttributeError``
+    to be raised in Jupyter or when trying to crop figures down to size with
+    Matplotlib 3.3 or 3.4 (but not 3.5).  For example, the following code would
+    previously crash with a message::
+
+      AttributeError: 'Arrow3D' object has no attribute '_path2d'
+
+    but will now succeed with all current supported versions of Matplotlib::
+
+      from qiskit.visualization import plot_bloch_vector
+      plot_bloch_vector([0, 1, 0]).savefig("tmp.png", bbox_inches='tight')