diff --git a/numpy/random/_generator.pyx b/numpy/random/_generator.pyx
index ee68810dd798..9bd09a2bca33 100644
--- a/numpy/random/_generator.pyx
+++ b/numpy/random/_generator.pyx
@@ -4408,6 +4408,7 @@ cdef class Generator:
             np.NPY_ARRAY_ALIGNED | np.NPY_ARRAY_C_CONTIGUOUS)
         if np.any(np.less(alpha_arr, 0)):
             raise ValueError('alpha < 0')
+
         alpha_data = <double*>np.PyArray_DATA(alpha_arr)
 
         if size is None:
@@ -4467,17 +4468,23 @@ cdef class Generator:
                 csum += alpha_data[j]
                 alpha_csum_data[j] = csum
 
-            with self.lock, nogil:
-                while i < totsize:
-                    acc = 1.
-                    for j in range(k - 1):
-                        v = random_beta(&self._bitgen, alpha_data[j],
-                                        alpha_csum_data[j + 1])
-                        val_data[i + j] = acc * v
-                        acc *= (1. - v)
-                    val_data[i + k - 1] = acc
-                    i = i + k
-
+            # If csum == 0, then all the values in alpha are 0, and there is
+            # nothing to do, because diric was created with np.zeros().
+            if csum > 0:
+                with self.lock, nogil:
+                    while i < totsize:
+                        acc = 1.
+                        for j in range(k - 1):
+                            v = random_beta(&self._bitgen, alpha_data[j],
+                                            alpha_csum_data[j + 1])
+                            val_data[i + j] = acc * v
+                            acc *= (1. - v)
+                            if alpha_csum_data[j + 1] == 0:
+                                # v must be 1, so acc is now 0. All
+                                # remaining elements will be left at 0.
+                                break
+                        val_data[i + k - 1] = acc
+                        i = i + k
         else:
             # Standard case: Unit normalisation of a vector of gamma random
             # variates
diff --git a/numpy/random/tests/test_generator_mt19937.py b/numpy/random/tests/test_generator_mt19937.py
index 1c57b3fa5d8d..e744f5ba611b 100644
--- a/numpy/random/tests/test_generator_mt19937.py
+++ b/numpy/random/tests/test_generator_mt19937.py
@@ -35,6 +35,7 @@
     },
 ]
 
+
 @pytest.fixture(scope='module', params=[True, False])
 def endpoint(request):
     return request.param
@@ -145,6 +146,7 @@ def test_multinomial_pvals_float32(self):
         with pytest.raises(ValueError, match=match):
             random.multinomial(1, pvals)
 
+
 class TestMultivariateHypergeometric:
 
     def setup_method(self):
@@ -1238,6 +1240,25 @@ def test_dirichlet_moderately_small_alpha(self):
         sample_mean = sample.mean(axis=0)
         assert_allclose(sample_mean, exact_mean, rtol=1e-3)
 
+    # This set of parameters includes inputs with alpha.max() >= 0.1 and
+    # alpha.max() < 0.1 to exercise both generation methods within the
+    # dirichlet code.
+    @pytest.mark.parametrize(
+        'alpha',
+        [[5, 9, 0, 8],
+         [0.5, 0, 0, 0],
+         [1, 5, 0, 0, 1.5, 0, 0, 0],
+         [0.01, 0.03, 0, 0.005],
+         [1e-5, 0, 0, 0],
+         [0.002, 0.015, 0, 0, 0.04, 0, 0, 0],
+         [0.0],
+         [0, 0, 0]],
+    )
+    def test_dirichlet_multiple_zeros_in_alpha(self, alpha):
+        alpha = np.array(alpha)
+        y = random.dirichlet(alpha)
+        assert_equal(y[alpha == 0], 0.0)
+
     def test_exponential(self):
         random = Generator(MT19937(self.seed))
         actual = random.exponential(1.1234, size=(3, 2))
@@ -1467,7 +1488,7 @@ def test_multivariate_normal(self, method):
                       mu, np.empty((3, 2)))
         assert_raises(ValueError, random.multivariate_normal,
                       mu, np.eye(3))
-        
+
     @pytest.mark.parametrize('mean, cov', [([0], [[1+1j]]), ([0j], [[1]])])
     def test_multivariate_normal_disallow_complex(self, mean, cov):
         random = Generator(MT19937(self.seed))
@@ -1847,7 +1868,6 @@ class TestBroadcast:
     def setup_method(self):
         self.seed = 123456789
 
-
     def test_uniform(self):
         random = Generator(MT19937(self.seed))
         low = [0]
diff --git a/numpy/random/tests/test_randomstate.py b/numpy/random/tests/test_randomstate.py
index 3099853d2a8e..524ac7b7c5e0 100644
--- a/numpy/random/tests/test_randomstate.py
+++ b/numpy/random/tests/test_randomstate.py
@@ -812,10 +812,6 @@ def test_dirichlet_bad_alpha(self):
         alpha = np.array([5.4e-01, -1.0e-16])
         assert_raises(ValueError, random.dirichlet, alpha)
 
-    def test_dirichlet_zero_alpha(self):
-        y = random.default_rng().dirichlet([5, 9, 0, 8])
-        assert_equal(y[2], 0)
-
     def test_dirichlet_alpha_non_contiguous(self):
         a = np.array([51.72840233779265162, -1.0, 39.74494232180943953])
         alpha = a[::2]
@@ -2061,6 +2057,7 @@ def test_randomstate_ctor_old_style_pickle():
     assert_equal(state_a['has_gauss'], state_b['has_gauss'])
     assert_equal(state_a['gauss'], state_b['gauss'])
 
+
 def test_hot_swap(restore_singleton_bitgen):
     # GH 21808
     def_bg = np.random.default_rng(0)