diff --git a/pandas/_libs/interval.pyi b/pandas/_libs/interval.pyi
index 4c36246e04d23..587fdf84f2f85 100644
--- a/pandas/_libs/interval.pyi
+++ b/pandas/_libs/interval.pyi
@@ -148,7 +148,7 @@ class Interval(IntervalMixin, Generic[_OrderableT]):
 
 def intervals_to_interval_bounds(
     intervals: np.ndarray, validate_closed: bool = ...
-) -> tuple[np.ndarray, np.ndarray, str]: ...
+) -> tuple[np.ndarray, np.ndarray, IntervalClosedType]: ...
 
 class IntervalTree(IntervalMixin):
     def __init__(
diff --git a/pandas/_libs/interval.pyx b/pandas/_libs/interval.pyx
index 14b7baf7f5a08..fe405b98f218c 100644
--- a/pandas/_libs/interval.pyx
+++ b/pandas/_libs/interval.pyx
@@ -612,7 +612,7 @@ def intervals_to_interval_bounds(ndarray intervals, bint validate_closed=True):
     tuple of
         left : ndarray
         right : ndarray
-        closed: str
+        closed: IntervalClosedType
     """
     cdef:
         object closed = None, interval
diff --git a/pandas/core/arrays/interval.py b/pandas/core/arrays/interval.py
index b8442205c331e..2ba66006a0645 100644
--- a/pandas/core/arrays/interval.py
+++ b/pandas/core/arrays/interval.py
@@ -226,7 +226,7 @@ def ndim(self) -> Literal[1]:
     def __new__(
         cls,
         data,
-        closed=None,
+        closed: IntervalClosedType | None = None,
         dtype: Dtype | None = None,
         copy: bool = False,
         verify_integrity: bool = True,
diff --git a/pandas/core/dtypes/dtypes.py b/pandas/core/dtypes/dtypes.py
index 479bfdc557a07..014d7a4c5a330 100644
--- a/pandas/core/dtypes/dtypes.py
+++ b/pandas/core/dtypes/dtypes.py
@@ -53,6 +53,7 @@
     from pandas._typing import (
         Dtype,
         DtypeObj,
+        IntervalClosedType,
         Ordered,
         npt,
         type_t,
@@ -1099,7 +1100,7 @@ class IntervalDtype(PandasExtensionDtype):
 
     _cache_dtypes: dict[str_type, PandasExtensionDtype] = {}
 
-    def __new__(cls, subtype=None, closed: str_type | None = None):
+    def __new__(cls, subtype=None, closed: IntervalClosedType | None = None):
         from pandas.core.dtypes.common import (
             is_string_dtype,
             pandas_dtype,
@@ -1137,7 +1138,7 @@ def __new__(cls, subtype=None, closed: str_type | None = None):
                                     "'closed' keyword does not match value "
                                     "specified in dtype string"
                                 )
-                        closed = gd["closed"]
+                        closed = gd["closed"]  # type: ignore[assignment]
 
             try:
                 subtype = pandas_dtype(subtype)
@@ -1175,7 +1176,7 @@ def _can_hold_na(self) -> bool:
         return True
 
     @property
-    def closed(self):
+    def closed(self) -> IntervalClosedType:
         return self._closed
 
     @property
diff --git a/pandas/core/indexes/interval.py b/pandas/core/indexes/interval.py
index 13c87a9d06b66..a667506135643 100644
--- a/pandas/core/indexes/interval.py
+++ b/pandas/core/indexes/interval.py
@@ -220,7 +220,7 @@ class IntervalIndex(ExtensionIndex):
     def __new__(
         cls,
         data,
-        closed=None,
+        closed: IntervalClosedType | None = None,
         dtype: Dtype | None = None,
         copy: bool = False,
         name: Hashable = None,
diff --git a/pandas/io/formats/style.py b/pandas/io/formats/style.py
index e2c5ed2ea92b6..8ddf14175a6da 100644
--- a/pandas/io/formats/style.py
+++ b/pandas/io/formats/style.py
@@ -65,6 +65,7 @@
         AxisInt,
         FilePath,
         IndexLabel,
+        IntervalClosedType,
         Level,
         QuantileInterpolation,
         Scalar,
@@ -3185,7 +3186,7 @@ def highlight_between(
         axis: Axis | None = 0,
         left: Scalar | Sequence | None = None,
         right: Scalar | Sequence | None = None,
-        inclusive: str = "both",
+        inclusive: IntervalClosedType = "both",
         props: str | None = None,
     ) -> Styler:
         """
@@ -3294,7 +3295,7 @@ def highlight_quantile(
         q_left: float = 0.0,
         q_right: float = 1.0,
         interpolation: QuantileInterpolation = "linear",
-        inclusive: str = "both",
+        inclusive: IntervalClosedType = "both",
         props: str | None = None,
     ) -> Styler:
         """