diff --git a/src/popup_input_filter.cpp b/src/popup_input_filter.cpp
index 1646e1b123..9d4336ffd8 100644
--- a/src/popup_input_filter.cpp
+++ b/src/popup_input_filter.cpp
@@ -95,6 +95,31 @@ bool PopupInputFilter::keyEvent(QKeyEvent *event)
     return true;
 }
 
+bool PopupInputFilter::touchDown(qint32 id, const QPointF &pos, quint32 time)
+{
+    Q_UNUSED(id)
+    Q_UNUSED(time)
+    if (m_popupClients.isEmpty()) {
+        return false;
+    }
+    auto pointerFocus = qobject_cast<AbstractClient*>(input()->findToplevel(pos.toPoint()));
+    if (!pointerFocus || !AbstractClient::belongToSameApplication(pointerFocus, qobject_cast<AbstractClient*>(m_popupClients.constLast()))) {
+        // a touch on a window (or no window) not belonging to the popup window
+        cancelPopups();
+        // filter out this touch
+        return true;
+    }
+    if (pointerFocus && pointerFocus->isDecorated()) {
+        // test whether it is on the decoration
+        const QRect clientRect = QRect(pointerFocus->clientPos(), pointerFocus->clientSize()).translated(pointerFocus->pos());
+        if (!clientRect.contains(pos.toPoint())) {
+            cancelPopups();
+            return true;
+        }
+    }
+    return false;
+}
+
 void PopupInputFilter::cancelPopups()
 {
     while (!m_popupClients.isEmpty()) {
diff --git a/src/popup_input_filter.h b/src/popup_input_filter.h
index a0a95446d2..7356ee595a 100644
--- a/src/popup_input_filter.h
+++ b/src/popup_input_filter.h
@@ -23,6 +23,7 @@ public:
     explicit PopupInputFilter();
     bool pointerEvent(QMouseEvent *event, quint32 nativeButton) override;
     bool keyEvent(QKeyEvent *event) override;
+    bool touchDown(qint32 id, const QPointF &pos, quint32 time) override;
 private:
     void handleClientAdded(Toplevel *client);
     void handleClientRemoved(Toplevel *client);