diff --git a/arrow/util.py b/arrow/util.py
index 7171d92c..1e341df0 100644
--- a/arrow/util.py
+++ b/arrow/util.py
@@ -1,6 +1,7 @@
 """Helpful functions used internally within arrow."""
 
 import datetime
+import math
 from typing import Any, Optional
 
 from dateutil.rrule import WEEKLY, rrule
@@ -43,16 +44,23 @@ def next_weekday(
 
 
 def is_timestamp(value: Any) -> bool:
-    """Check if value is a valid timestamp."""
+    """Check if value is a valid timestamp.
+
+    A value is considered a valid timestamp when it is an ``int``, ``float``,
+    or ``str`` that parses via :func:`float` to a finite real number. ``bool``
+    is rejected (it is technically an ``int`` subclass). Non-finite floats —
+    ``inf``, ``-inf``, and ``nan`` — are rejected because they cannot be
+    converted into a real datetime.
+    """
     if isinstance(value, bool):
         return False
     if not isinstance(value, (int, float, str)):
         return False
     try:
-        float(value)
-        return True
+        parsed = float(value)
     except ValueError:
         return False
+    return math.isfinite(parsed)
 
 
 def validate_ordinal(value: Any) -> None:
diff --git a/tests/test_util.py b/tests/test_util.py
index 2454dac5..fbb28edf 100644
--- a/tests/test_util.py
+++ b/tests/test_util.py
@@ -56,6 +56,21 @@ class InvalidTimestamp:
         full_datetime = "2019-06-23T13:12:42"
         assert not util.is_timestamp(full_datetime)
 
+    def test_is_timestamp_rejects_non_finite(self):
+        # Non-finite floats (inf/-inf/nan) cannot be turned into a real
+        # datetime, so is_timestamp must not treat them as a valid timestamp
+        # and let them reach the regex- or float()-driven downstream paths.
+        assert not util.is_timestamp(float("inf"))
+        assert not util.is_timestamp(float("-inf"))
+        assert not util.is_timestamp(float("nan"))
+        assert not util.is_timestamp("inf")
+        assert not util.is_timestamp("-inf")
+        assert not util.is_timestamp("nan")
+        assert not util.is_timestamp("Infinity")
+        assert not util.is_timestamp("NaN")
+        # A literal that overflows float() into +inf must be rejected too.
+        assert not util.is_timestamp("1e1000")
+
     def test_validate_ordinal(self):
         timestamp_float = 1607066816.815537
         timestamp_int = int(timestamp_float)