diff --git a/doc/source/whatsnew/v3.0.0.rst b/doc/source/whatsnew/v3.0.0.rst
index b5bd3216dd990..78dfea820481a 100644
--- a/doc/source/whatsnew/v3.0.0.rst
+++ b/doc/source/whatsnew/v3.0.0.rst
@@ -649,6 +649,7 @@ Datetimelike
 - Bug in :meth:`DatetimeIndex.union` and :meth:`DatetimeIndex.intersection` when ``unit`` was non-nanosecond (:issue:`59036`)
 - Bug in :meth:`Series.dt.microsecond` producing incorrect results for pyarrow backed :class:`Series`. (:issue:`59154`)
 - Bug in :meth:`to_datetime` not respecting dayfirst if an uncommon date string was passed. (:issue:`58859`)
+- Bug in :meth:`to_datetime` on float array with missing values throwing ``FloatingPointError`` (:issue:`58419`)
 - Bug in :meth:`to_datetime` on float32 df with year, month, day etc. columns leads to precision issues and incorrect result. (:issue:`60506`)
 - Bug in :meth:`to_datetime` reports incorrect index in case of any failure scenario. (:issue:`58298`)
 - Bug in :meth:`to_datetime` wrongly converts when ``arg`` is a ``np.datetime64`` object with unit of ``ps``. (:issue:`60341`)
diff --git a/pandas/_libs/tslibs/conversion.pyx b/pandas/_libs/tslibs/conversion.pyx
index 7a8b4df447aee..c4acf72ab87d8 100644
--- a/pandas/_libs/tslibs/conversion.pyx
+++ b/pandas/_libs/tslibs/conversion.pyx
@@ -137,7 +137,7 @@ def cast_from_unit_vectorized(
 
     out = np.empty(shape, dtype="i8")
     base = np.empty(shape, dtype="i8")
-    frac = np.empty(shape, dtype="f8")
+    frac = np.zeros(shape, dtype="f8")
 
     for i in range(len(values)):
         if is_nan(values[i]):
diff --git a/pandas/tests/tools/test_to_datetime.py b/pandas/tests/tools/test_to_datetime.py
index e039f54960389..616ae36c989be 100644
--- a/pandas/tests/tools/test_to_datetime.py
+++ b/pandas/tests/tools/test_to_datetime.py
@@ -2520,6 +2520,15 @@ def test_to_datetime_overflow(self):
         with pytest.raises(OutOfBoundsTimedelta, match=msg):
             date_range(start="1/1/1700", freq="B", periods=100000)
 
+    def test_to_datetime_float_with_nans_floating_point_error(self):
+        # GH#58419
+        ser = Series([np.nan] * 1000 + [1712219033.0], dtype=np.float64)
+        result = to_datetime(ser, unit="s", errors="coerce")
+        expected = Series(
+            [NaT] * 1000 + [Timestamp("2024-04-04 08:23:53")], dtype="datetime64[ns]"
+        )
+        tm.assert_series_equal(result, expected)
+
     def test_string_invalid_operation(self, cache):
         invalid = np.array(["87156549591102612381000001219H5"], dtype=object)
         # GH #51084