TV photos showed the Kallisto navy vessel tilting and sinking on its side and a substantial part of its stern was missing. A tug boat later towed it to the naval base of Salamina.
Two individuals were slightly wounded and transported to hospital, a coast guard official said , adding that the 27-member crew of the Greek navy vessel was taken to safety.
The container ship Maersk Launceston, 266 metres long, was not harmed.
How the collision occurred was not immediately clear, said the official. The port authorities of Piraeus, which initiated the investigation, temporarily barred the container ship from sailing.
Maritime Business World