diff --git a/src/lightning/fabric/loggers/tensorboard.py b/src/lightning/fabric/loggers/tensorboard.py
index 208244dc38cd3..c159c81854e8e 100644
--- a/src/lightning/fabric/loggers/tensorboard.py
+++ b/src/lightning/fabric/loggers/tensorboard.py
@@ -203,19 +203,22 @@ def log_metrics(self, metrics: Mapping[str, float], step: Optional[int] = None)
         metrics = _add_prefix(metrics, self._prefix, self.LOGGER_JOIN_CHAR)
 
         for k, v in metrics.items():
-            if isinstance(v, Tensor):
+            if isinstance(v, Tensor) and v.ndim == 0:
                 v = v.item()
 
-            if isinstance(v, dict):
-                self.experiment.add_scalars(k, v, step)
-            else:
-                try:
+            try:
+                if isinstance(v, dict):
+                    self.experiment.add_scalars(k, v, step)
+                elif isinstance(v, Tensor):
+                    self.experiment.add_histogram(k, v, step)
+                else:
                     self.experiment.add_scalar(k, v, step)
-                # TODO(fabric): specify the possible exception
-                except Exception as ex:
-                    raise ValueError(
-                        f"\n you tried to log {v} which is currently not supported. Try a dict or a scalar/tensor."
-                    ) from ex
+
+            # TODO(fabric): specify the possible exception
+            except Exception as ex:
+                raise ValueError(
+                    f"\n you tried to log {v} which is currently not supported. Try a dict or a scalar/tensor."
+                ) from ex
 
     @override
     @rank_zero_only
diff --git a/src/lightning/pytorch/CHANGELOG.md b/src/lightning/pytorch/CHANGELOG.md
index 8eef1c0e7c6e8..2996c0267de46 100644
--- a/src/lightning/pytorch/CHANGELOG.md
+++ b/src/lightning/pytorch/CHANGELOG.md
@@ -27,6 +27,9 @@ The format is based on [Keep a Changelog](http://keepachangelog.com/en/1.0.0/).
 
 ### Changed
 
+- Allow `LightningModule` to log `Tensorboard` histograms ([#19851](https://github.com/Lightning-AI/pytorch-lightning/pull/19851))
+
+
 - Default to `RichProgressBar` and `RichModelSummary` if the rich package is available. Fallback to TQDMProgressBar and ModelSummary otherwise ([#20896](https://github.com/Lightning-AI/pytorch-lightning/pull/20896))
 
 
diff --git a/src/lightning/pytorch/core/module.py b/src/lightning/pytorch/core/module.py
index 85f631ee40f75..1c4aa081a2ca3 100644
--- a/src/lightning/pytorch/core/module.py
+++ b/src/lightning/pytorch/core/module.py
@@ -661,10 +661,12 @@ def __to_tensor(self, value: Union[Tensor, numbers.Number], name: str) -> Tensor
             if isinstance(value, Tensor)
             else torch.tensor(value, device=self.device, dtype=_get_default_dtype())
         )
-        if not torch.numel(value) == 1:
+
+        # check tensor contains single element (implies value.ndim == 0), or is a non-empty 1D array
+        if not (torch.numel(value) == 1 or (torch.numel(value) > 0 and value.ndim == 1)):
             raise ValueError(
-                f"`self.log({name}, {value})` was called, but the tensor must have a single element."
-                f" You can try doing `self.log({name}, {value}.mean())`"
+                f"`self.log({name}, {value})` was called, but the tensor must have a single element, "
+                f"or a single non-empty dimension. You can try doing `self.log({name}, {value}.mean())`"
             )
         value = value.squeeze()
         return value
diff --git a/tests/tests_pytorch/loggers/test_tensorboard.py b/tests/tests_pytorch/loggers/test_tensorboard.py
index 7e02a73c93082..fc347cb560c76 100644
--- a/tests/tests_pytorch/loggers/test_tensorboard.py
+++ b/tests/tests_pytorch/loggers/test_tensorboard.py
@@ -153,7 +153,13 @@ def name(self):
 @pytest.mark.parametrize("step_idx", [10, None])
 def test_tensorboard_log_metrics(tmp_path, step_idx):
     logger = TensorBoardLogger(tmp_path)
-    metrics = {"float": 0.3, "int": 1, "FloatTensor": torch.tensor(0.1), "IntTensor": torch.tensor(1)}
+    metrics = {
+        "float": 0.3,
+        "int": 1,
+        "FloatTensor": torch.tensor(0.1),
+        "IntTensor": torch.tensor(1),
+        "Histogram": torch.tensor([10, 100, 1000]),
+    }
     logger.log_metrics(metrics, step_idx)
 
 
diff --git a/tests/tests_pytorch/trainer/logging_/test_train_loop_logging.py b/tests/tests_pytorch/trainer/logging_/test_train_loop_logging.py
index 6916eae68e9c0..2120a628e7980 100644
--- a/tests/tests_pytorch/trainer/logging_/test_train_loop_logging.py
+++ b/tests/tests_pytorch/trainer/logging_/test_train_loop_logging.py
@@ -640,10 +640,18 @@ def training_step(self, *args):
 
     class TestModel(BoringModel):
         def on_train_start(self):
-            self.log("foo", torch.tensor([1.0, 2.0]))
+            self.log("foo", torch.tensor([]))  # empty
 
     model = TestModel()
-    with pytest.raises(ValueError, match="tensor must have a single element"):
+    with pytest.raises(ValueError, match="tensor must have a single element, or a single non-empty dimension."):
+        trainer.fit(model)
+
+    class TestModel(BoringModel):
+        def on_train_start(self):
+            self.log("foo", torch.tensor([[1.0], [2.0]]))  # too-many dimensions
+
+    model = TestModel()
+    with pytest.raises(ValueError, match="tensor must have a single element, or a single non-empty dimension."):
         trainer.fit(model)