diff --git a/src/pytorch_lightning/CHANGELOG.md b/src/pytorch_lightning/CHANGELOG.md
index 5bd34c2864..5c064c5296 100644
--- a/src/pytorch_lightning/CHANGELOG.md
+++ b/src/pytorch_lightning/CHANGELOG.md
@@ -54,6 +54,8 @@ The format is based on [Keep a Changelog](http://keepachangelog.com/en/1.0.0/).
 
 - Fixed an issue with the `BaseFinetuning` callback not setting the `track_running_stats` attribute for batch normaliztion layers ([#15063](https://github.com/Lightning-AI/lightning/pull/15063))
 
+- Fixed an issue with `WandbLogger(log_model=True|'all)` raising an error and not being able to serialize tensors in the metadata ([#15544](https://github.com/Lightning-AI/lightning/pull/15544))
+
 
 ## [1.8.0] - 2022-11-01
 
diff --git a/src/pytorch_lightning/loggers/wandb.py b/src/pytorch_lightning/loggers/wandb.py
index 5d60989c65..55757487d7 100644
--- a/src/pytorch_lightning/loggers/wandb.py
+++ b/src/pytorch_lightning/loggers/wandb.py
@@ -22,6 +22,7 @@ from typing import Any, Dict, List, Mapping, Optional, Union
 
 import torch.nn as nn
 from lightning_utilities.core.imports import RequirementCache
+from torch import Tensor
 
 from pytorch_lightning.callbacks import Checkpoint
 from pytorch_lightning.loggers.logger import Logger, rank_zero_experiment
@@ -572,7 +573,7 @@ class WandbLogger(Logger):
         for t, p, s, tag in checkpoints:
             metadata = (
                 {
-                    "score": s,
+                    "score": s.item() if isinstance(s, Tensor) else s,
                     "original_filename": Path(p).name,
                     checkpoint_callback.__class__.__name__: {
                         k: getattr(checkpoint_callback, k)
diff --git a/tests/tests_pytorch/loggers/test_wandb.py b/tests/tests_pytorch/loggers/test_wandb.py
index ec7661aadb..3ce1401efa 100644
--- a/tests/tests_pytorch/loggers/test_wandb.py
+++ b/tests/tests_pytorch/loggers/test_wandb.py
@@ -19,6 +19,7 @@ import pytest
 
 import pytorch_lightning
 from pytorch_lightning import Trainer
+from pytorch_lightning.callbacks import ModelCheckpoint
 from pytorch_lightning.demos.boring_classes import BoringModel
 from pytorch_lightning.loggers import WandbLogger
 from pytorch_lightning.utilities.exceptions import MisconfigurationException
@@ -251,6 +252,40 @@ def test_wandb_log_model(wandb, monkeypatch, tmpdir):
     )
 
 
+@mock.patch("pytorch_lightning.loggers.wandb.Run", new=mock.Mock)
+@mock.patch("pytorch_lightning.loggers.wandb.wandb")
+def test_wandb_log_model_with_score(wandb, monkeypatch, tmpdir):
+    """Test to prevent regression on #15543, ensuring the score is logged as a Python number, not a scalar
+    tensor."""
+    monkeypatch.setattr(pytorch_lightning.loggers.wandb, "_WANDB_GREATER_EQUAL_0_10_22", True)
+
+    wandb.run = None
+    model = BoringModel()
+
+    wandb.init().log_artifact.reset_mock()
+    wandb.init.reset_mock()
+    wandb.Artifact.reset_mock()
+    logger = WandbLogger(log_model=True)
+    logger.experiment.id = "1"
+    logger.experiment.name = "run_name"
+    checkpoint_callback = ModelCheckpoint(monitor="step")
+    trainer = Trainer(
+        default_root_dir=tmpdir,
+        logger=logger,
+        callbacks=[checkpoint_callback],
+        max_epochs=1,
+        limit_train_batches=3,
+        limit_val_batches=1,
+    )
+    trainer.fit(model)
+
+    calls = wandb.Artifact.call_args_list
+    assert len(calls) == 1
+    score = calls[0][1]["metadata"]["score"]
+    # model checkpoint monitors scalar tensors, but wandb can't serializable them - expect Python scalars in metadata
+    assert isinstance(score, int) and score == 3
+
+
 @mock.patch("pytorch_lightning.loggers.wandb.Run", new=mock.Mock)
 @mock.patch("pytorch_lightning.loggers.wandb.wandb")
 def test_wandb_log_media(wandb, tmpdir):