diff --git a/doc/source/whatsnew/v3.0.0.rst b/doc/source/whatsnew/v3.0.0.rst
index 865996bdf8892..54dfbe47607fe 100644
--- a/doc/source/whatsnew/v3.0.0.rst
+++ b/doc/source/whatsnew/v3.0.0.rst
@@ -454,6 +454,7 @@ Datetimelike
 - Bug in :func:`date_range` where the last valid timestamp would sometimes not be produced (:issue:`56134`)
 - Bug in :func:`date_range` where using a negative frequency value would not include all points between the start and end values (:issue:`56382`)
 - Bug in :func:`tseries.api.guess_datetime_format` would fail to infer time format when "%Y" == "%H%M" (:issue:`57452`)
+- Bug in :meth:`Dataframe.agg` with df with missing values resulting in IndexError (:issue:`58810`)
 - Bug in :meth:`DatetimeIndex.is_year_start` and :meth:`DatetimeIndex.is_quarter_start` does not raise on Custom business days frequencies bigger then "1C" (:issue:`58664`)
 - Bug in :meth:`DatetimeIndex.is_year_start` and :meth:`DatetimeIndex.is_quarter_start` returning ``False`` on double-digit frequencies (:issue:`58523`)
 - Bug in setting scalar values with mismatched resolution into arrays with non-nanosecond ``datetime64``, ``timedelta64`` or :class:`DatetimeTZDtype` incorrectly truncating those scalars (:issue:`56410`)
diff --git a/pandas/core/apply.py b/pandas/core/apply.py
index 25836e967e948..82e3b24202347 100644
--- a/pandas/core/apply.py
+++ b/pandas/core/apply.py
@@ -1825,11 +1825,13 @@ def relabel_result(
                 com.get_callable_name(f) if not isinstance(f, str) else f for f in fun
             ]
             col_idx_order = Index(s.index).get_indexer(fun)
-            s = s.iloc[col_idx_order]
-
+            valid_idx = col_idx_order != -1
+            if valid_idx.any():
+                s = s.iloc[col_idx_order[valid_idx]]
         # assign the new user-provided "named aggregation" as index names, and reindex
         # it based on the whole user-provided names.
-        s.index = reordered_indexes[idx : idx + len(fun)]
+        if not s.empty:
+            s.index = reordered_indexes[idx : idx + len(fun)]
         reordered_result_in_dict[col] = s.reindex(columns)
         idx = idx + len(fun)
     return reordered_result_in_dict
diff --git a/pandas/tests/groupby/aggregate/test_aggregate.py b/pandas/tests/groupby/aggregate/test_aggregate.py
index 3362d6209af6d..0b1de7fd353f6 100644
--- a/pandas/tests/groupby/aggregate/test_aggregate.py
+++ b/pandas/tests/groupby/aggregate/test_aggregate.py
@@ -62,6 +62,32 @@ def test_agg_ser_multi_key(df):
     tm.assert_series_equal(results, expected)
 
 
+def test_agg_with_missing_values():
+    # GH#58810
+    missing_df = DataFrame(
+        {
+            "nan": [np.nan, np.nan, np.nan, np.nan],
+            "na": [pd.NA, pd.NA, pd.NA, pd.NA],
+            "nat": [pd.NaT, pd.NaT, pd.NaT, pd.NaT],
+            "none": [None, None, None, None],
+            "values": [1, 2, 3, 4],
+        }
+    )
+
+    result = missing_df.agg(x=("nan", "min"), y=("na", "min"), z=("values", "sum"))
+
+    expected = DataFrame(
+        {
+            "nan": [np.nan, np.nan, np.nan],
+            "na": [np.nan, np.nan, np.nan],
+            "values": [np.nan, np.nan, 10.0],
+        },
+        index=["x", "y", "z"],
+    )
+
+    tm.assert_frame_equal(result, expected)
+
+
 def test_groupby_aggregation_mixed_dtype():
     # GH 6212
     expected = DataFrame(