diff --git a/homeassistant/components/sensor/__init__.py b/homeassistant/components/sensor/__init__.py
index c00d20d51ef..b8151256519 100644
--- a/homeassistant/components/sensor/__init__.py
+++ b/homeassistant/components/sensor/__init__.py
@@ -8,7 +8,7 @@ from dataclasses import dataclass
 from datetime import UTC, date, datetime, timedelta
 from decimal import Decimal, InvalidOperation as DecimalInvalidOperation
 import logging
-from math import ceil, floor, log10
+from math import ceil, floor, isfinite, log10
 from typing import Any, Final, Self, cast, final
 
 from homeassistant.config_entries import ConfigEntry
@@ -582,7 +582,11 @@ class SensorEntity(Entity):
         if not isinstance(value, (int, float, Decimal)):
             try:
                 if isinstance(value, str) and "." not in value and "e" not in value:
-                    numerical_value = int(value)
+                    try:
+                        numerical_value = int(value)
+                    except ValueError:
+                        # Handle nan, inf
+                        numerical_value = float(value)
                 else:
                     numerical_value = float(value)  # type:ignore[arg-type]
             except (TypeError, ValueError) as err:
@@ -596,6 +600,15 @@ class SensorEntity(Entity):
         else:
             numerical_value = value
 
+        if not isfinite(numerical_value):
+            raise ValueError(
+                f"Sensor {self.entity_id} has device class '{device_class}', "
+                f"state class '{state_class}' unit '{unit_of_measurement}' and "
+                f"suggested precision '{suggested_precision}' thus indicating it "
+                f"has a numeric value; however, it has the non-finite value: "
+                f"'{numerical_value}'"
+            )
+
         if native_unit_of_measurement != unit_of_measurement and (
             converter := UNIT_CONVERTERS.get(device_class)
         ):
diff --git a/tests/components/sensor/test_init.py b/tests/components/sensor/test_init.py
index 530e8cb4209..1f836ad9095 100644
--- a/tests/components/sensor/test_init.py
+++ b/tests/components/sensor/test_init.py
@@ -1861,13 +1861,17 @@ async def test_device_classes_with_invalid_unit_of_measurement(
     ],
 )
 @pytest.mark.parametrize(
-    "native_value",
+    ("native_value", "problem"),
     [
-        "",
-        "abc",
-        "13.7.1",
-        datetime(2012, 11, 10, 7, 35, 1),
-        date(2012, 11, 10),
+        ("", "non-numeric"),
+        ("abc", "non-numeric"),
+        ("13.7.1", "non-numeric"),
+        (datetime(2012, 11, 10, 7, 35, 1), "non-numeric"),
+        (date(2012, 11, 10), "non-numeric"),
+        ("inf", "non-finite"),
+        (float("inf"), "non-finite"),
+        ("nan", "non-finite"),
+        (float("nan"), "non-finite"),
     ],
 )
 async def test_non_numeric_validation_error(
@@ -1875,6 +1879,7 @@ async def test_non_numeric_validation_error(
     caplog: pytest.LogCaptureFixture,
     enable_custom_integrations: None,
     native_value: Any,
+    problem: str,
     device_class: SensorDeviceClass | None,
     state_class: SensorStateClass | None,
     unit: str | None,
@@ -1899,7 +1904,7 @@ async def test_non_numeric_validation_error(
 
     assert (
         "thus indicating it has a numeric value; "
-        f"however, it has the non-numeric value: '{native_value}'"
+        f"however, it has the {problem} value: '{native_value}'"
     ) in caplog.text