diff --git a/src/core/geometry/qgsgeometry.cpp b/src/core/geometry/qgsgeometry.cpp
index ad7979fbd5e3..03ae4403f2f3 100644
--- a/src/core/geometry/qgsgeometry.cpp
+++ b/src/core/geometry/qgsgeometry.cpp
@@ -388,7 +388,7 @@ QgsPointXY QgsGeometry::closestVertex( const QgsPointXY &point, int &atVertex, i
     return QgsPointXY();
   }
 
-  QgsPoint pt( point.x(), point.y() );
+  QgsPoint pt( point );
   QgsVertexId id;
 
   QgsPoint vp = QgsGeometryUtils::closestVertex( *( d->geometry ), pt, id );
@@ -630,7 +630,7 @@ double QgsGeometry::closestVertexWithContext( const QgsPointXY &point, int &atVe
   }
 
   QgsVertexId vId;
-  QgsPoint pt( point.x(), point.y() );
+  QgsPoint pt( point );
   QgsPoint closestPoint = QgsGeometryUtils::closestVertex( *( d->geometry ), pt, vId );
   if ( !vId.isValid() )
     return -1;
diff --git a/src/core/geometry/qgsgeometryutils.cpp b/src/core/geometry/qgsgeometryutils.cpp
index 6b49f4e0f51f..c7a7e815e87b 100644
--- a/src/core/geometry/qgsgeometryutils.cpp
+++ b/src/core/geometry/qgsgeometryutils.cpp
@@ -71,6 +71,9 @@ QgsPoint QgsGeometryUtils::closestVertex( const QgsAbstractGeometry &geom, const
   QgsPoint minDistPoint;
   id = QgsVertexId(); // set as invalid
 
+  if ( geom.isEmpty() || pt.isEmpty() )
+    return minDistPoint;
+
   QgsVertexId vertexId;
   QgsPoint vertex;
   while ( geom.nextVertex( vertexId, vertex ) )
diff --git a/src/core/geometry/qgspoint.cpp b/src/core/geometry/qgspoint.cpp
index 2dd528fe31ad..6c91df6d48c1 100644
--- a/src/core/geometry/qgspoint.cpp
+++ b/src/core/geometry/qgspoint.cpp
@@ -67,6 +67,11 @@ QgsPoint::QgsPoint( const QgsPointXY &p )
   , mM( std::numeric_limits<double>::quiet_NaN() )
 {
   mWkbType = QgsWkbTypes::Point;
+  if ( p.isEmpty() )
+  {
+    mX = std::numeric_limits<double>::quiet_NaN();
+    mY = std::numeric_limits<double>::quiet_NaN();
+  }
 }
 
 QgsPoint::QgsPoint( QPointF p )
diff --git a/tests/src/python/test_qgsgeometry.py b/tests/src/python/test_qgsgeometry.py
index 6073f48f25b7..709290305e84 100644
--- a/tests/src/python/test_qgsgeometry.py
+++ b/tests/src/python/test_qgsgeometry.py
@@ -1193,6 +1193,10 @@ def testClosestVertex(self):
         assert abs(dist - exp) < 0.00001, "Expected: %f; Got:%f" % (exp, dist)
         self.assertEqual(leftOf, -1)
 
+        (point, atVertex, beforeVertex, afterVertex, dist) = polygon.closestVertex(QgsPointXY())
+        self.assertTrue(point.isEmpty())
+        self.assertEqual(dist, -1)
+
         (point, atVertex, beforeVertex, afterVertex, dist) = QgsGeometry().closestVertex(QgsPointXY(42, 42))
         self.assertTrue(point.isEmpty())
 
diff --git a/tests/src/python/test_qgspoint.py b/tests/src/python/test_qgspoint.py
index e2770ebf2096..a895c5940f42 100644
--- a/tests/src/python/test_qgspoint.py
+++ b/tests/src/python/test_qgspoint.py
@@ -86,6 +86,10 @@ def test_issue_32443(self):
         p = QgsPoint(1, 2, m=4, z=3)
         assert p.wkbType() == QgsWkbTypes.PointZM and p.x() == 1 and p.y() == 2 and p.z() == 3 and p.m() == 4
 
+    def test_empty_QgsPointXY(self):
+        p = QgsPoint(QgsPointXY())
+        assert p.isEmpty()
+
 
 class TestQgsPoint(unittest.TestCase):