diff --git a/pandas/core/internals/blocks.py b/pandas/core/internals/blocks.py
index ca81d54a0fb86..a8e7224eb524f 100644
--- a/pandas/core/internals/blocks.py
+++ b/pandas/core/internals/blocks.py
@@ -869,6 +869,12 @@ def _replace_coerce(
 
     # ---------------------------------------------------------------------
 
+    def _maybe_squeeze_arg(self, arg: np.ndarray) -> np.ndarray:
+        """
+        For compatibility with 1D-only ExtensionArrays.
+        """
+        return arg
+
     def setitem(self, indexer, value):
         """
         Attempt self.values[indexer] = value, possibly creating a new array.
@@ -1314,6 +1320,46 @@ class EABackedBlock(Block):
 
     values: ExtensionArray
 
+    def putmask(self, mask, new) -> list[Block]:
+        """
+        See Block.putmask.__doc__
+        """
+        mask = extract_bool_array(mask)
+
+        values = self.values
+
+        mask = self._maybe_squeeze_arg(mask)
+
+        try:
+            # Caller is responsible for ensuring matching lengths
+            values._putmask(mask, new)
+        except (TypeError, ValueError) as err:
+            if isinstance(err, ValueError) and "Timezones don't match" not in str(err):
+                # TODO(2.0): remove catching ValueError at all since
+                #  DTA raising here is deprecated
+                raise
+
+            if is_interval_dtype(self.dtype):
+                # Discussion about what we want to support in the general
+                #  case GH#39584
+                blk = self.coerce_to_target_dtype(new)
+                if blk.dtype == _dtype_obj:
+                    # For now at least, only support casting e.g.
+                    #  Interval[int64]->Interval[float64],
+                    raise
+                return blk.putmask(mask, new)
+
+            elif isinstance(self, NDArrayBackedExtensionBlock):
+                # NB: not (yet) the same as
+                #  isinstance(values, NDArrayBackedExtensionArray)
+                blk = self.coerce_to_target_dtype(new)
+                return blk.putmask(mask, new)
+
+            else:
+                raise
+
+        return [self]
+
     def delete(self, loc) -> None:
         """
         Delete given loc(-s) from block in-place.
@@ -1410,36 +1456,16 @@ def set_inplace(self, locs, values) -> None:
             # _cache not yet initialized
             pass
 
-    def putmask(self, mask, new) -> list[Block]:
+    def _maybe_squeeze_arg(self, arg):
         """
-        See Block.putmask.__doc__
+        If necessary, squeeze a (N, 1) ndarray to (N,)
         """
-        mask = extract_bool_array(mask)
-
-        new_values = self.values
-
-        if mask.ndim == new_values.ndim + 1:
+        # e.g. if we are passed a 2D mask for putmask
+        if isinstance(arg, np.ndarray) and arg.ndim == self.values.ndim + 1:
             # TODO(EA2D): unnecessary with 2D EAs
-            mask = mask.reshape(new_values.shape)
-
-        try:
-            # Caller is responsible for ensuring matching lengths
-            new_values._putmask(mask, new)
-        except TypeError:
-            if not is_interval_dtype(self.dtype):
-                # Discussion about what we want to support in the general
-                #  case GH#39584
-                raise
-
-            blk = self.coerce_to_target_dtype(new)
-            if blk.dtype == _dtype_obj:
-                # For now at least, only support casting e.g.
-                #  Interval[int64]->Interval[float64],
-                raise
-            return blk.putmask(mask, new)
-
-        nb = type(self)(new_values, placement=self._mgr_locs, ndim=self.ndim)
-        return [nb]
+            assert arg.shape[1] == 1
+            arg = arg[:, 0]
+        return arg
 
     @property
     def is_view(self) -> bool:
@@ -1595,15 +1621,8 @@ def where(self, other, cond) -> list[Block]:
         cond = extract_bool_array(cond)
         assert not isinstance(other, (ABCIndex, ABCSeries, ABCDataFrame))
 
-        if isinstance(other, np.ndarray) and other.ndim == 2:
-            # TODO(EA2D): unnecessary with 2D EAs
-            assert other.shape[1] == 1
-            other = other[:, 0]
-
-        if isinstance(cond, np.ndarray) and cond.ndim == 2:
-            # TODO(EA2D): unnecessary with 2D EAs
-            assert cond.shape[1] == 1
-            cond = cond[:, 0]
+        other = self._maybe_squeeze_arg(other)
+        cond = self._maybe_squeeze_arg(cond)
 
         if lib.is_scalar(other) and isna(other):
             # The default `other` for Series / Frame is np.nan
@@ -1698,16 +1717,6 @@ def setitem(self, indexer, value):
         values[indexer] = value
         return self
 
-    def putmask(self, mask, new) -> list[Block]:
-        mask = extract_bool_array(mask)
-
-        if not self._can_hold_element(new):
-            return self.coerce_to_target_dtype(new).putmask(mask, new)
-
-        arr = self.values
-        arr.T._putmask(mask, new)
-        return [self]
-
     def where(self, other, cond) -> list[Block]:
         arr = self.values