The police were sent to enforce an emergency government order that took effect at 0400 GMT to force the strikers back to work.
Television footage showed a cordon of riot police deployed at the harbour to keep a strike support force away from ships taking on passengers and cargo.
The Panhellenic Seamen’s Union (PNO) is protesting against a labour reform that allows ferry owners to regulate the number of crew members depending on the distance of the voyage.
The union also notes that its sector is suffering heavy unemployment while some 2,000 of its members have been unpaid by employers for six months.
PNO had decided to extend the six-day mobilisation for another 48 hours before the government crackdown.
“The government made every possible effort to satisfy the maritime workers’ demands,” Merchant Marine Minister Costis Moussouroulis told reporters on Tuesday.
“Unfortunately, petty politics have left no room for dialogue,” Moussouroulis said.
Greece’s largest private-sector union GSEE has called an Athens-wide strike on Wednesday in support of PNO, a move that will disrupt public transport in the capital.
The seamen’s strike had cut off Greece’s islands from resupplying with goods and medicine.
An island trade association on Tuesday pleaded with the seamen to end their mobilisation.
“The islands have reached their limits,” the Cycladic chamber of commerce said in a statement, adding: “This undeclared war must end.”
PNO claims that unemployment in the sector has hit more than 7,000 maritime workers, out of a total of 15,000 active workers.
As the coalition government tries to implement a harsh austerity programme demanded by international creditors in return for vital rescue loans, it has had to deal with waves of strikes.
Riot police had also been sent in January to break a strike by Athens metro staff that had paralysed the network for nine days.