diff --git a/src/lightning/pytorch/CHANGELOG.md b/src/lightning/pytorch/CHANGELOG.md
index 8bc8e45989f77..03ec83f189f23 100644
--- a/src/lightning/pytorch/CHANGELOG.md
+++ b/src/lightning/pytorch/CHANGELOG.md
@@ -16,6 +16,8 @@ The format is based on [Keep a Changelog](http://keepachangelog.com/en/1.0.0/).
 
 - Fix CSVLogger logging hyperparameter at every write which increase latency  ([#20594](https://github.com/Lightning-AI/pytorch-lightning/pull/20594))
 
+- Fix OverflowError when resuming from checkpoint with an iterable dataset ([#20565](https://github.com/Lightning-AI/pytorch-lightning/issues/20565))
+
 
 ## [2.5.0] - 2024-12-19
 
diff --git a/src/lightning/pytorch/loops/evaluation_loop.py b/src/lightning/pytorch/loops/evaluation_loop.py
index d007466ee3b1c..7f033dbd8e2c2 100644
--- a/src/lightning/pytorch/loops/evaluation_loop.py
+++ b/src/lightning/pytorch/loops/evaluation_loop.py
@@ -11,6 +11,7 @@
 # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 # See the License for the specific language governing permissions and
 # limitations under the License.
+import math
 import os
 import shutil
 import sys
@@ -268,7 +269,10 @@ def increment_progress_to_evaluation_end(self) -> None:
         if self.skip:
             return
         self.reset()
-        max_batch = int(max(self.max_batches))
+        max_batch = max(self.max_batches)
+        if isinstance(max_batch, float) and math.isinf(max_batch):
+            return
+        max_batch = int(max_batch)
         if max_batch == -1:
             return
         self.batch_progress.increment_by(max_batch, True)
diff --git a/tests/tests_pytorch/checkpointing/test_model_checkpoint.py b/tests/tests_pytorch/checkpointing/test_model_checkpoint.py
index 2351cc7548f79..1907a5fb35799 100644
--- a/tests/tests_pytorch/checkpointing/test_model_checkpoint.py
+++ b/tests/tests_pytorch/checkpointing/test_model_checkpoint.py
@@ -30,12 +30,13 @@
 import yaml
 from jsonargparse import ArgumentParser
 from torch import optim
+from torch.utils.data.dataloader import DataLoader
 
 import lightning.pytorch as pl
 from lightning.fabric.utilities.cloud_io import _load as pl_load
 from lightning.pytorch import Trainer, seed_everything
 from lightning.pytorch.callbacks import ModelCheckpoint
-from lightning.pytorch.demos.boring_classes import BoringModel
+from lightning.pytorch.demos.boring_classes import BoringModel, RandomIterableDataset
 from lightning.pytorch.loggers import CSVLogger, TensorBoardLogger
 from lightning.pytorch.utilities.exceptions import MisconfigurationException
 from lightning.pytorch.utilities.imports import _OMEGACONF_AVAILABLE
@@ -1624,3 +1625,44 @@ def test_save_last_cli(val, expected):
     parser.add_argument("--a", type=annot)
     args = parser.parse_args(["--a", val])
     assert args.a == expected
+
+
+def test_load_with_inf_data_loader(tmp_path):
+    """Test loading from a checkpoint with a dataloader that does not have a length."""
+    # Test for https://github.com/Lightning-AI/pytorch-lightning/issues/20565
+    dataset = RandomIterableDataset(size=32, count=10)
+
+    class ModelWithIterableDataset(BoringModel):
+        def train_dataloader(self) -> DataLoader:
+            return DataLoader(dataset)
+
+        def val_dataloader(self) -> DataLoader:
+            return DataLoader(dataset)
+
+    model = ModelWithIterableDataset()
+    with pytest.raises(TypeError):
+        len(model.train_dataloader())
+
+    trainer_kwargs = {
+        "default_root_dir": tmp_path,
+        "max_epochs": 2,
+        "limit_train_batches": 2,
+        "limit_val_batches": None,
+        "check_val_every_n_epoch": 1,
+        "enable_model_summary": False,
+        "logger": False,
+    }
+    mc_kwargs = {
+        "save_last": True,
+        "every_n_train_steps": 1,
+    }
+    trainer = Trainer(**trainer_kwargs, callbacks=ModelCheckpoint(**mc_kwargs))
+    trainer.fit(model)
+
+    checkpoint_path = tmp_path / "checkpoints" / "epoch=1-step=4.ckpt"
+    assert checkpoint_path.name in os.listdir(tmp_path / "checkpoints")
+
+    # Resume from checkpoint and run for more epochs
+    trainer_kwargs["max_epochs"] = 4
+    trainer = Trainer(**trainer_kwargs, callbacks=ModelCheckpoint(**mc_kwargs))
+    trainer.fit(model, ckpt_path=checkpoint_path)