diff --git a/botorch/models/fully_bayesian.py b/botorch/models/fully_bayesian.py
index 27d066ef00..954fa4097d 100644
--- a/botorch/models/fully_bayesian.py
+++ b/botorch/models/fully_bayesian.py
@@ -178,14 +178,15 @@ def sample(self) -> None:
         lengthscale = self.sample_lengthscale(dim=self.ard_num_dims, **tkwargs)
         K = matern52_kernel(X=self.train_X, lengthscale=lengthscale)
         K = outputscale * K + noise * torch.eye(self.train_X.shape[0], **tkwargs)
-        pyro.sample(
-            "Y",
-            pyro.distributions.MultivariateNormal(
-                loc=mean.view(-1).expand(self.train_X.shape[0]),
-                covariance_matrix=K,
-            ),
-            obs=self.train_Y.squeeze(-1),
-        )
+        if self.train_Y.shape[-2] > 0:
+            pyro.sample(
+                "Y",
+                pyro.distributions.MultivariateNormal(
+                    loc=mean.view(-1).expand(self.train_X.shape[0]),
+                    covariance_matrix=K,
+                ),
+                obs=self.train_Y.squeeze(-1),
+            )
 
     def sample_outputscale(
         self, concentration: float = 2.0, rate: float = 0.15, **tkwargs: Any
diff --git a/test/models/test_fully_bayesian.py b/test/models/test_fully_bayesian.py
index 3ea029c310..7a33f4f9da 100644
--- a/test/models/test_fully_bayesian.py
+++ b/test/models/test_fully_bayesian.py
@@ -387,6 +387,16 @@ def test_fit_model(self):
             self.assertIsNone(model.covar_module)
             self.assertIsNone(model.likelihood)
 
+    def test_empty(self):
+        model = SaasFullyBayesianSingleTaskGP(
+            train_X=torch.rand(0, 3),
+            train_Y=torch.rand(0, 1),
+        )
+        fit_fully_bayesian_model_nuts(
+            model, warmup_steps=2, num_samples=6, thinning=3, disable_progbar=True
+        )
+        self.assertEqual(model.covar_module.outputscale.shape, torch.Size([2]))
+
     def test_transforms(self):
         for infer_noise in [True, False]:
             tkwargs = {"device": self.device, "dtype": torch.double}