diff --git a/py-polars/polars/testing/parametric/strategies/core.py b/py-polars/polars/testing/parametric/strategies/core.py
index b90e759ee3fb..22e8d7c65d5b 100644
--- a/py-polars/polars/testing/parametric/strategies/core.py
+++ b/py-polars/polars/testing/parametric/strategies/core.py
@@ -420,6 +420,7 @@ def dataframes(  # noqa: D417
             version="1.0.0",
         )
         min_size = max_size = size
+    allow_nan = kwargs.pop("allow_nan", None)
 
     if isinstance(include_cols, column):
         include_cols = [include_cols]
@@ -451,6 +452,11 @@ def dataframes(  # noqa: D417
                 c.allow_null = allow_null.get(c.name, True)
             else:
                 c.allow_null = allow_null
+        if c.allow_nan is None:
+            if isinstance(allow_nan, Mapping):
+                c.allow_nan = allow_nan.get(c.name, True)
+            else:
+                c.allow_nan = allow_nan
 
     allow_series_chunks = draw(st.booleans()) if allow_chunks else False
 
@@ -464,6 +470,7 @@ def dataframes(  # noqa: D417
                     max_size=size,
                     strategy=c.strategy,
                     allow_null=c.allow_null,  # type: ignore[arg-type]
+                    allow_nan=c.allow_nan,
                     allow_chunks=allow_series_chunks,
                     unique=c.unique,
                     allowed_dtypes=allowed_dtypes,
@@ -503,6 +510,8 @@ class column:
         supports overriding the default strategy for the given dtype.
     allow_null : bool, optional
         Allow nulls as possible values and allow the `Null` data type by default.
+    allow_nan : bool, optional
+        Allow nans as possible values. Only applicable to float/decimal dtype columns.
     unique : bool, optional
         flag indicating that all values generated for the column should be unique.
 
@@ -540,6 +549,7 @@ class column:
     dtype: PolarsDataType | None = None
     strategy: SearchStrategy[Any] | None = None
     allow_null: bool | None = None
+    allow_nan: bool | None = None
     unique: bool = False
 
     null_probability: float | None = None
diff --git a/py-polars/polars/testing/parametric/strategies/data.py b/py-polars/polars/testing/parametric/strategies/data.py
index 1f0c656cf73f..6186ac82d30f 100644
--- a/py-polars/polars/testing/parametric/strategies/data.py
+++ b/py-polars/polars/testing/parametric/strategies/data.py
@@ -94,10 +94,17 @@ def integers(
 
 
 def floats(
-    bit_width: Literal[32, 64] = 64, *, allow_infinity: bool = True
+    bit_width: Literal[32, 64] = 64,
+    *,
+    allow_infinity: bool = True,
+    allow_nan: bool = True,
 ) -> SearchStrategy[float]:
     """Create a strategy for generating integers."""
-    return st.floats(width=bit_width, allow_infinity=allow_infinity)
+    return st.floats(
+        width=bit_width,
+        allow_infinity=allow_infinity,
+        allow_nan=allow_nan,
+    )
 
 
 def booleans() -> SearchStrategy[bool]:
@@ -382,9 +389,17 @@ def data(
     if (strategy := _STATIC_STRATEGIES.get(dtype.base_type())) is not None:
         strategy = strategy
     elif dtype == Float32:
-        strategy = floats(32, allow_infinity=kwargs.pop("allow_infinity", True))
+        strategy = floats(
+            32,
+            allow_infinity=kwargs.pop("allow_infinity", True),
+            allow_nan=kwargs.pop("allow_nan", True),
+        )
     elif dtype == Float64:
-        strategy = floats(64, allow_infinity=kwargs.pop("allow_infinity", True))
+        strategy = floats(
+            64,
+            allow_infinity=kwargs.pop("allow_infinity", True),
+            allow_nan=kwargs.pop("allow_nan", True),
+        )
     elif dtype == Datetime:
         strategy = datetimes(
             time_unit=getattr(dtype, "time_unit", None) or "us",
diff --git a/py-polars/tests/unit/testing/parametric/strategies/test_core.py b/py-polars/tests/unit/testing/parametric/strategies/test_core.py
index bb54255f4d10..ebc5a3dda2f0 100644
--- a/py-polars/tests/unit/testing/parametric/strategies/test_core.py
+++ b/py-polars/tests/unit/testing/parametric/strategies/test_core.py
@@ -68,6 +68,18 @@ def test_series_allow_null_allowed_dtypes(s: pl.Series) -> None:
     assert s.dtype == pl.Null
 
 
+@given(
+    s=series(
+        allowed_dtypes=[pl.Float32, pl.Float64],
+        allow_nan=False,
+        allow_null=False,
+        min_size=1,
+    )
+)
+def test_series_allow_nan_false(s: pl.Series) -> None:
+    assert s.is_not_nan().any()
+
+
 @given(s=series(allowed_dtypes=[pl.List(pl.Int8)], allow_null=False))
 def test_series_allow_null_nested(s: pl.Series) -> None:
     for v in s:
@@ -115,6 +127,33 @@ def test_dataframes_allow_null_column(df: pl.DataFrame) -> None:
     assert 0 <= null_count <= df.height * df.width
 
 
+@given(
+    df=dataframes(
+        cols=1,
+        allowed_dtypes=[pl.Float32, pl.Float64],
+        allow_nan=False,
+    ),
+)
+def test_dataframes_allow_nan_false_global(df: pl.DataFrame) -> None:
+    print(df)
+    nan_count = df.select(pl.col("col0").is_nan().sum()).item()
+    assert nan_count == 0
+
+
+@given(
+    df=dataframes(
+        cols=2,
+        allowed_dtypes=[pl.Float32, pl.Float64],
+        allow_nan={"col0": False},
+    ),
+)
+def test_dataframes_allow_nan_false_column(df: pl.DataFrame) -> None:
+    print(df)
+    nan_count = sum(df.select(pl.all().is_nan().sum()).row(0))
+    # The maximum nan count is all values in a single column.
+    assert 0 <= nan_count <= df.height
+
+
 @given(
     df=dataframes(
         cols=1,