diff --git a/doc/whats_new/v1.0.rst b/doc/whats_new/v1.0.rst
index d8776653cd9e8..92983b0041b74 100644
--- a/doc/whats_new/v1.0.rst
+++ b/doc/whats_new/v1.0.rst
@@ -2,6 +2,23 @@
 
 .. currentmodule:: sklearn
 
+.. _changes_1_0_1:
+
+Version 1.0.1
+=============
+
+**In Development**
+
+Changelog
+---------
+
+:mod:`sklearn.calibration`
+..........................
+
+- |Fix| Fixed :class:`calibration.CalibratedClassifierCV` to handle correctly
+  `sample_weight` when `ensemble=False`.
+  :pr:`20638` by :user:`Julien Bohné <JulienB-78>`.
+
 .. _changes_1_0:
 
 Version 1.0.0
diff --git a/sklearn/calibration.py b/sklearn/calibration.py
index 9ede41a775c3e..700f1ed6cc397 100644
--- a/sklearn/calibration.py
+++ b/sklearn/calibration.py
@@ -351,6 +351,11 @@ def fit(self, X, y, sample_weight=None):
             else:
                 this_estimator = clone(base_estimator)
                 _, method_name = _get_prediction_method(this_estimator)
+                fit_params = (
+                    {"sample_weight": sample_weight}
+                    if sample_weight is not None and supports_sw
+                    else None
+                )
                 pred_method = partial(
                     cross_val_predict,
                     estimator=this_estimator,
@@ -359,6 +364,7 @@ def fit(self, X, y, sample_weight=None):
                     cv=cv,
                     method=method_name,
                     n_jobs=self.n_jobs,
+                    fit_params=fit_params,
                 )
                 predictions = _compute_predictions(
                     pred_method, method_name, X, n_classes
diff --git a/sklearn/tests/test_calibration.py b/sklearn/tests/test_calibration.py
index 040571df4681b..da1645a1c0fd6 100644
--- a/sklearn/tests/test_calibration.py
+++ b/sklearn/tests/test_calibration.py
@@ -166,6 +166,12 @@ def test_sample_weight(data, method, ensemble):
     X_train, y_train, sw_train = X[:n_samples], y[:n_samples], sample_weight[:n_samples]
     X_test = X[n_samples:]
 
+    scaler = StandardScaler()
+    X_train = scaler.fit_transform(
+        X_train
+    )  # compute mean, std and transform training data as well
+    X_test = scaler.transform(X_test)
+
     base_estimator = LinearSVC(random_state=42)
     calibrated_clf = CalibratedClassifierCV(
         base_estimator, method=method, ensemble=ensemble
@@ -182,6 +188,68 @@ def test_sample_weight(data, method, ensemble):
     assert diff > 0.1
 
 
+@pytest.mark.parametrize("method", ["sigmoid", "isotonic"])
+@pytest.mark.parametrize("ensemble", [True, False])
+def test_sample_weight_class_imbalanced(method, ensemble):
+    """Use an imbalanced dataset to check that `sample_weight` is taken into
+    account in the calibration estimator."""
+    X, y = make_blobs((100, 1000), center_box=(-1, 1), random_state=42)
+
+    # Compute weights to compensate for the unbalance of the dataset
+    weights = np.array([0.9, 0.1])
+    sample_weight = weights[(y == 1).astype(int)]
+
+    X_train, X_test, y_train, y_test, sw_train, sw_test = train_test_split(
+        X, y, sample_weight, stratify=y, random_state=42
+    )
+
+    # FIXME: ideally we should create a `Pipeline` with the `StandardScaler`
+    # followed by the `LinearSVC`. However, `Pipeline` does not expose
+    # `sample_weight` and it will be silently ignored.
+    scaler = StandardScaler()
+    X_train = scaler.fit_transform(X_train)
+    X_test = scaler.transform(X_test)
+
+    base_estimator = LinearSVC(random_state=42)
+    calibrated_clf = CalibratedClassifierCV(
+        base_estimator, method=method, ensemble=ensemble
+    )
+    calibrated_clf.fit(X_train, y_train, sample_weight=sw_train)
+    predictions = calibrated_clf.predict_proba(X_test)[:, 1]
+
+    assert brier_score_loss(y_test, predictions, sample_weight=sw_test) < 0.2
+
+
+@pytest.mark.parametrize("method", ["sigmoid", "isotonic"])
+def test_sample_weight_class_imbalanced_ensemble_equivalent(method):
+    X, y = make_blobs((100, 1000), center_box=(-1, 1), random_state=42)
+
+    # Compute weigths to compensate the unbalance of the dataset
+    sample_weight = 9 * (y == 0) + 1
+
+    X_train, X_test, y_train, y_test, sw_train, sw_test = train_test_split(
+        X, y, sample_weight, stratify=y, random_state=42
+    )
+
+    scaler = StandardScaler()
+    X_train = scaler.fit_transform(
+        X_train
+    )  # compute mean, std and transform training data as well
+    X_test = scaler.transform(X_test)
+
+    predictions = []
+    for ensemble in [True, False]:
+        base_estimator = LinearSVC(random_state=42)
+        calibrated_clf = CalibratedClassifierCV(
+            base_estimator, method=method, ensemble=ensemble
+        )
+        calibrated_clf.fit(X_train, y_train, sample_weight=sw_train)
+        predictions.append(calibrated_clf.predict_proba(X_test)[:, 1])
+
+    diff = np.linalg.norm(predictions[0] - predictions[1])
+    assert diff < 1.5
+
+
 @pytest.mark.parametrize("method", ["sigmoid", "isotonic"])
 @pytest.mark.parametrize("ensemble", [True, False])
 def test_parallel_execution(data, method, ensemble):