diff --git a/doc/whats-new.rst b/doc/whats-new.rst
index e4c3a4d533f..6223dd678ea 100644
--- a/doc/whats-new.rst
+++ b/doc/whats-new.rst
@@ -58,6 +58,8 @@ New Features
 
 Bug fixes
 ~~~~~~~~~
+- ``ValueError`` is raised when ``fill_value`` is not a scalar in :py:meth:`full_like`. (:issue`3977`)
+  By `Huite Bootsma <https://github.com/huite>`_.
 - Fix wrong order in converting a ``pd.Series`` with a MultiIndex to ``DataArray``. (:issue:`3951`)
   By `Keisuke Fujii <https://github.com/fujiisoup>`_.
 - Fix renaming of coords when one or more stacked coords is not in
diff --git a/xarray/core/common.py b/xarray/core/common.py
index 8f6d57e9f12..1e7069ec51f 100644
--- a/xarray/core/common.py
+++ b/xarray/core/common.py
@@ -25,7 +25,7 @@
 from .options import OPTIONS, _get_keep_attrs
 from .pycompat import dask_array_type
 from .rolling_exp import RollingExp
-from .utils import Frozen, either_dict_or_kwargs
+from .utils import Frozen, either_dict_or_kwargs, is_scalar
 
 # Used as a sentinel value to indicate a all dimensions
 ALL_DIMS = ...
@@ -1397,6 +1397,9 @@ def full_like(other, fill_value, dtype: DTypeLike = None):
     from .dataset import Dataset
     from .variable import Variable
 
+    if not is_scalar(fill_value):
+        raise ValueError(f"fill_value must be scalar. Received {fill_value} instead.")
+
     if isinstance(other, Dataset):
         data_vars = {
             k: _full_like_variable(v, fill_value, dtype)
diff --git a/xarray/tests/test_variable.py b/xarray/tests/test_variable.py
index 78e3848b8fb..3003e0d66f3 100644
--- a/xarray/tests/test_variable.py
+++ b/xarray/tests/test_variable.py
@@ -2213,6 +2213,10 @@ def test_full_like(self):
         assert expect.dtype == bool
         assert_identical(expect, full_like(orig, True, dtype=bool))
 
+        # raise error on non-scalar fill_value
+        with raises_regex(ValueError, "must be scalar"):
+            full_like(orig, [1.0, 2.0])
+
     @requires_dask
     def test_full_like_dask(self):
         orig = Variable(