diff --git a/src/lightning/pytorch/loops/fit_loop.py b/src/lightning/pytorch/loops/fit_loop.py
index 31d6724a043a3..065237c5dffcd 100644
--- a/src/lightning/pytorch/loops/fit_loop.py
+++ b/src/lightning/pytorch/loops/fit_loop.py
@@ -204,6 +204,11 @@ def skip(self) -> bool:
         # so we cannot use it solely
         return self.done or self.trainer.limit_train_batches == 0
 
+    @property
+    def _is_resuming(self) -> bool:
+        """Whether we're resuming training from a checkpoint."""
+        return self._loaded_from_state_dict
+
     def run(self) -> None:
         self.setup_data()
         if self.skip:
diff --git a/src/lightning/pytorch/loops/training_epoch_loop.py b/src/lightning/pytorch/loops/training_epoch_loop.py
index 7cdf7888bbfe2..b542631d15048 100644
--- a/src/lightning/pytorch/loops/training_epoch_loop.py
+++ b/src/lightning/pytorch/loops/training_epoch_loop.py
@@ -235,7 +235,11 @@ def reset(self) -> None:
 
     def on_run_start(self, data_fetcher: _DataFetcher) -> None:
         # `iter()` was called once in `FitLoop.setup_data()` already
-        if self.trainer.current_epoch > 0 and not self.restarting:
+        # Only call iter() if:
+        # 1. Not restarting AND
+        # 2. Not resuming from checkpoint (not _is_resuming) AND
+        # 3. Past first epoch (current_epoch > 0)
+        if (self.trainer.current_epoch > 0 and not self.trainer.fit_loop._is_resuming) and not self.restarting:
             iter(data_fetcher)  # creates the iterator inside the fetcher
 
         # add the previous `fetched` value to properly track `is_last_batch` with no prefetching
diff --git a/tests/tests_pytorch/loops/test_double_iter_in_iterable_dataset.py b/tests/tests_pytorch/loops/test_double_iter_in_iterable_dataset.py
new file mode 100644
index 0000000000000..1deb169da7206
--- /dev/null
+++ b/tests/tests_pytorch/loops/test_double_iter_in_iterable_dataset.py
@@ -0,0 +1,81 @@
+# Copyright The Lightning AI team.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# 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.
+#
+# This test tests the resuming of training from a checkpoint file using an IterableDataset.
+# And contains code mentioned in the issue: #19427.
+# Ref: https://github.com/Lightning-AI/pytorch-lightning/issues/19427
+import multiprocessing as mp
+import os
+from collections.abc import Iterator
+from pathlib import Path
+from queue import Queue
+
+import numpy as np
+from torch.utils.data import DataLoader, IterableDataset
+
+from lightning.pytorch import Trainer
+from lightning.pytorch.demos.boring_classes import BoringModel
+
+
+class QueueDataset(IterableDataset):
+    def __init__(self, queue: Queue) -> None:
+        super().__init__()
+        self.queue = queue
+
+    def __iter__(self) -> Iterator:
+        for _ in range(5):
+            tensor, _ = self.queue.get(timeout=5)
+            yield tensor
+
+
+def create_queue() -> Queue:
+    q = mp.Queue()
+    arr = np.random.random([1, 32]).astype(np.float32)
+    for ind in range(20):
+        q.put((arr, ind))
+    return q
+
+
+def train_model(queue: Queue, max_epochs: int, ckpt_path: Path) -> Trainer:
+    dataloader = DataLoader(QueueDataset(queue), num_workers=1, batch_size=None, persistent_workers=True)
+    trainer = Trainer(
+        max_epochs=max_epochs,
+        enable_progress_bar=False,
+        enable_checkpointing=False,
+        devices=1,
+        logger=False,
+    )
+    if ckpt_path.exists():
+        trainer.fit(BoringModel(), dataloader, ckpt_path=str(ckpt_path))
+    else:
+        trainer.fit(BoringModel(), dataloader)
+        trainer.save_checkpoint(str(ckpt_path))
+    return trainer
+
+
+def test_resume_training_with(tmp_path):
+    """Test resuming training from checkpoint file using a IterableDataset."""
+    queue = create_queue()
+    max_epoch = 2
+    ckpt_path = tmp_path / "model.ckpt"
+    trainer = train_model(queue, max_epoch, ckpt_path)
+    assert trainer is not None
+
+    assert os.path.exists(ckpt_path), f"Checkpoint file '{ckpt_path}' wasn't created"
+
+    ckpt_size = os.path.getsize(ckpt_path)
+    assert ckpt_size > 0, f"Checkpoint file is empty (size: {ckpt_size} bytes)"
+
+    trainer = train_model(queue, max_epoch + 2, ckpt_path)
+    assert trainer is not None