diff --git a/lib/matplotlib/axes/_axes.py b/lib/matplotlib/axes/_axes.py
@@ -3,6 +3,7 @@
 import logging
 import math
 from numbers import Integral, Number
+from datetime import timedelta
 
 import numpy as np
 from numpy import ma
@@ -3180,7 +3181,7 @@ def errorbar(self, x, y, yerr=None, xerr=None,
               errors.
             - *None*: No errorbar.
 
-            Note that all error arrays should have *positive* values.
+            Note that all error arrays should have *non-negative* values.
 
             See :doc:`/gallery/statistics/errorbar_features`
             for an example on the usage of ``xerr`` and ``yerr``.
@@ -3284,6 +3285,18 @@ def errorbar(self, x, y, yerr=None, xerr=None,
         if len(x) != len(y):
             raise ValueError("'x' and 'y' must have the same size")
 
+        def has_negative_values(array):
+            if array is None:
+                return False
+            try:
+                return np.any(array < 0)
+            except TypeError:  # if array contains 'datetime.timedelta' types
+                return np.any(array < timedelta(0))
+
+        if has_negative_values(xerr) or has_negative_values(yerr):
+            raise ValueError(
+                "'xerr' and 'yerr' must have non-negative values")
+
         if isinstance(errorevery, Integral):
             errorevery = (0, errorevery)
         if isinstance(errorevery, tuple):

diff --git a/lib/matplotlib/tests/test_axes.py b/lib/matplotlib/tests/test_axes.py
@@ -3513,6 +3513,25 @@ def test_errorbar_every_invalid():
         ax.errorbar(x, y, yerr, errorevery='foobar')
 
 
+def test_xerr_yerr_positive():
+    ax = plt.figure().subplots()
+
+    error_message = "'xerr' and 'yerr' must have non-negative values"
+
+    with pytest.raises(ValueError, match=error_message):
+        ax.errorbar(x=[0], y=[0], xerr=[[-0.5], [1]], yerr=[[-0.5], [1]])
+    with pytest.raises(ValueError, match=error_message):
+        ax.errorbar(x=[0], y=[0], xerr=[[-0.5], [1]])
+    with pytest.raises(ValueError, match=error_message):
+        ax.errorbar(x=[0], y=[0], yerr=[[-0.5], [1]])
+    with pytest.raises(ValueError, match=error_message):
+        x = np.arange(5)
+        y = [datetime.datetime(2021, 9, i * 2 + 1) for i in x]
+        ax.errorbar(x=x,
+                    y=y,
+                    yerr=datetime.timedelta(days=-10))
+
+
 @check_figures_equal()
 def test_errorbar_every(fig_test, fig_ref):
     x = np.linspace(0, 1, 15)