Hundreds of protesters waving Turkish flags gathered outside, demanding to see the minister.
Dutch police used dogs and water cannon early on Sunday to disperse the crowd, which threw bottles and stones.
Several demonstrators were beaten by police with batons. They carried out charges on horseback, while officers advanced on foot with shields and armoured vans.
Less than a day after Dutch authorities prevented Foreign Minister Mevlut Cavusoglu flying to Rotterdam, Turkey’s family minister, Fatma Betul Sayan Kaya, said on Twitter she was being escorted back to Germany.
“The world must take a stance in the name of democracy against this fascist act! This behaviour against a female minister can never be accepted,” she said.
The Rotterdam mayor confirmed she was being escorted by police to the German border.
Kaya later boarded a private plane from the German town of Cologne to return to Istanbul, mass-circulating newspaper Hurriyet said.
The Dutch government, which stands to lose heavily to the anti-Islam party of Geert Wilders in elections next week, said it considered the visits undesirable and “the Netherlands could not cooperate in the public political campaigning of Turkish ministers in the Netherlands”.
The government said it saw the potential to import divisions into its own Turkish minority, which has both pro- and anti-Erdogan camps.
Dutch politicians across the spectrum said they supported Prime Minister Mark Rutte’s decision to ban the visits.
In a statement issued early on Sunday, Prime Minister Binali Yildirim said Turkey had told Dutch authorities it would retaliate in the “harshest ways” and “respond in kind to this unacceptable behaviour”.
Turkey’s foreign ministry said it did not want the Dutch ambassador to Ankara to return from leave “for some time”.
Turkish authorities sealed off the Dutch embassy in Ankara and consulate in Istanbul in apparent retaliation and hundreds gathered there for protests at the Dutch action.
Erdogan is looking to the large number of emigre Turks living in Europe, especially in Germany and the Netherlands, to help clinch victory next month in a referendum that would give him sweeping new powers.
German Chancellor Angela Merkel has said she will do everything possible to prevent Turkish political tensions spilling onto German soil.
Four rallies in Austria and one in Switzerland have been cancelled due to the growing dispute.
Erdogan has cited domestic threats from Kurdish and Islamist militants and a July coup bid as cause to vote “yes” to his new powers.
But he has also drawn on the emotionally charged row with Europe to portray Turkey as betrayed by allies while facing wars on its southern borders.
Netherlands slams ‘irresponsible’ Turkish minister
The Netherlands criticised a Turkish minister as “irresponsible” for attempting to visit after being told she was not welcome and hit out at “unacceptable” verbal attacks by Turkish authorities amid an escalating row with Ankara.
The Dutch government said it had told Turkey it could not compromise on public order and security.
“The search for a reasonable solution proved impossible, and the verbal attacks that followed today from the Turkish authorities are unacceptable,” it said in a statement.
“In this context Minster Kaya’s visit was irresponsible. Through contacts with the Turkish authorities, the message was repeatedly conveyed that Minister Kaya is not welcome in the Netherlands… nevertheless she decided to travel.”
The Hague had also refused to allow Foreign Minister Mevlut Cavusoglu’s plane to land ahead of a rally, with Turkey’s President Recep Tayyip Erdogan likening the ban to Nazism.
The Netherlands is home to some 400,000 people of Turkish origin, and Ankara is keen to harness votes of the diaspora in Europe ahead of an April 16 referendum on boosting presidential powers.