diff --git a/RELEASE-NOTES.md b/RELEASE-NOTES.md
index 6e1f0b46a4..f76d5fddb4 100644
--- a/RELEASE-NOTES.md
+++ b/RELEASE-NOTES.md
@@ -33,6 +33,7 @@ It also brings some dreadfully awaited fixes, so be sure to go through the chang
 - Fixed `MatrixNormal` random method to work with parameters as random variables. (see [#4368](https://github.com/pymc-devs/pymc3/pull/4368))
 - Update the `logcdf` method of several continuous distributions to return -inf for invalid parameters and values, and raise an informative error when multiple values cannot be evaluated in a single call. (see [4393](https://github.com/pymc-devs/pymc3/pull/4393))
 - Improve numerical stability in `logp` and `logcdf` methods of `ExGaussian` (see [#4407](https://github.com/pymc-devs/pymc3/pull/4407))
+- Issue UserWarning when doing prior or posterior predictive sampling with models containing Potential factors (see [#4419](https://github.com/pymc-devs/pymc3/pull/4419))
 
 ## PyMC3 3.10.0 (7 December 2020)
 
diff --git a/pymc3/distributions/posterior_predictive.py b/pymc3/distributions/posterior_predictive.py
index 2366077fb0..4d6c1f4596 100644
--- a/pymc3/distributions/posterior_predictive.py
+++ b/pymc3/distributions/posterior_predictive.py
@@ -222,6 +222,14 @@ def fast_sample_posterior_predictive(
 
     model = modelcontext(model)
     assert model is not None
+
+    if model.potentials:
+        warnings.warn(
+            "The effect of Potentials on other parameters is ignored during posterior predictive sampling. "
+            "This is likely to lead to invalid or biased predictive samples.",
+            UserWarning,
+        )
+
     with model:
 
         if keep_size and samples is not None:
diff --git a/pymc3/sampling.py b/pymc3/sampling.py
index 0dedb87723..cd3db3233f 100644
--- a/pymc3/sampling.py
+++ b/pymc3/sampling.py
@@ -1692,6 +1692,13 @@ def sample_posterior_predictive(
 
     model = modelcontext(model)
 
+    if model.potentials:
+        warnings.warn(
+            "The effect of Potentials on other parameters is ignored during posterior predictive sampling. "
+            "This is likely to lead to invalid or biased predictive samples.",
+            UserWarning,
+        )
+
     if var_names is not None:
         vars_ = [model[x] for x in var_names]
     else:
@@ -1791,6 +1798,15 @@ def sample_posterior_predictive_w(
     if models is None:
         models = [modelcontext(models)] * len(traces)
 
+    for model in models:
+        if model.potentials:
+            warnings.warn(
+                "The effect of Potentials on other parameters is ignored during posterior predictive sampling. "
+                "This is likely to lead to invalid or biased predictive samples.",
+                UserWarning,
+            )
+            break
+
     if weights is None:
         weights = [1] * len(traces)
 
@@ -1903,6 +1919,13 @@ def sample_prior_predictive(
     """
     model = modelcontext(model)
 
+    if model.potentials:
+        warnings.warn(
+            "The effect of Potentials on other parameters is ignored during prior predictive sampling. "
+            "This is likely to lead to invalid or biased predictive samples.",
+            UserWarning,
+        )
+
     if var_names is None:
         prior_pred_vars = model.observed_RVs
         prior_vars = (
diff --git a/pymc3/tests/test_sampling.py b/pymc3/tests/test_sampling.py
index 0decbbd1c9..c95ad230cb 100644
--- a/pymc3/tests/test_sampling.py
+++ b/pymc3/tests/test_sampling.py
@@ -722,6 +722,21 @@ def test_variable_type(self):
             assert ppc["a"].dtype.kind == "f"
             assert ppc["b"].dtype.kind == "i"
 
+    def test_potentials_warning(self):
+        warning_msg = "The effect of Potentials on other parameters is ignored during"
+        with pm.Model() as m:
+            a = pm.Normal("a", 0, 1)
+            p = pm.Potential("p", a + 1)
+            obs = pm.Normal("obs", a, 1, observed=5)
+
+        trace = az.from_dict({"a": np.random.rand(10)})
+        with m:
+            with pytest.warns(UserWarning, match=warning_msg):
+                pm.sample_posterior_predictive(trace, samples=5)
+
+            with pytest.warns(UserWarning, match=warning_msg):
+                pm.fast_sample_posterior_predictive(trace, samples=5)
+
 
 class TestSamplePPCW(SeededTest):
     def test_sample_posterior_predictive_w(self):
@@ -773,6 +788,17 @@ def test_sample_posterior_predictive_w(self):
         ):
             pm.sample_posterior_predictive_w([trace_0, trace_2], 100, [model_0, model_2])
 
+    def test_potentials_warning(self):
+        warning_msg = "The effect of Potentials on other parameters is ignored during"
+        with pm.Model() as m:
+            a = pm.Normal("a", 0, 1)
+            p = pm.Potential("p", a + 1)
+            obs = pm.Normal("obs", a, 1, observed=5)
+
+        trace = az.from_dict({"a": np.random.rand(10)})
+        with pytest.warns(UserWarning, match=warning_msg):
+            pm.sample_posterior_predictive_w(samples=5, traces=[trace, trace], models=[m, m])
+
 
 @pytest.mark.parametrize(
     "method",
@@ -1012,6 +1038,16 @@ def test_bounded_dist(self):
             prior_trace = pm.sample_prior_predictive(5)
             assert prior_trace["x"].shape == (5, 3, 1)
 
+    def test_potentials_warning(self):
+        warning_msg = "The effect of Potentials on other parameters is ignored during"
+        with pm.Model() as m:
+            a = pm.Normal("a", 0, 1)
+            p = pm.Potential("p", a + 1)
+
+        with m:
+            with pytest.warns(UserWarning, match=warning_msg):
+                pm.sample_prior_predictive(samples=5)
+
 
 class TestSamplePosteriorPredictive:
     def test_point_list_arg_bug_fspp(self, point_list_arg_bug_fixture):