diff --git a/qiskit_ibm_runtime/estimator.py b/qiskit_ibm_runtime/estimator.py
index aa571622a..18daa09fd 100644
--- a/qiskit_ibm_runtime/estimator.py
+++ b/qiskit_ibm_runtime/estimator.py
@@ -189,7 +189,12 @@ def run(
         Returns:
             Submitted job.
 
+        Raises:
+            ValueError: if precision value is not strictly greater than 0.
         """
+        if precision is not None:
+            if precision <= 0:
+                raise ValueError("The precision value must be strictly greater than 0.")
         coerced_pubs = [EstimatorPub.coerce(pub, precision) for pub in pubs]
         validate_estimator_pubs(coerced_pubs)
         return self._run(coerced_pubs)  # type: ignore[arg-type]
diff --git a/test/unit/test_estimator.py b/test/unit/test_estimator.py
index e9fb10d21..723507f4c 100644
--- a/test/unit/test_estimator.py
+++ b/test/unit/test_estimator.py
@@ -112,6 +112,17 @@ def test_unsupported_values_for_estimator_options(self):
                     inst.options.update(**bad_opt)
                 self.assertIn(list(bad_opt.keys())[0], str(exc.exception))
 
+    def test_invalid_estimator_precision_option(self):
+        """Test exception when precision is invalid."""
+
+        backend = get_mocked_backend()
+        backend.configuration().simulator = True
+
+        estimator = EstimatorV2(backend=backend)
+        with self.assertRaises(ValueError) as exc:
+            estimator.run(**get_primitive_inputs(estimator), precision=0)
+        self.assertIn("The precision value must be strictly greater than 0", str(exc.exception))
+
     def test_pec_simulator(self):
         """Test error is raised when using pec on simulator without coupling map."""
         backend = get_mocked_backend()