The fishery patrol boat entered the 12-nautical mile zone off Kubajima, one of the Senkaku islands, at about 3:36 pm (local time), according to a statement.
It added that the ship moved out of the zone after 22 minutes, watched by a Japanese coastguard vessel.
Beijing claims the islands, which it calls the Diaoyus.
The incident was the latest in a series, with Japan claiming that in one case Chinese vessels locked weapons-targeting radar onto a ship and a helicopter. Beijing denied the charge.
In an interview with The Washington Post before the trip, Abe said a tighter alliance with the United States would send a message to Beijing in the tense row over the disputed territory.
The dispute between Asia's two largest economies intensified in September when Tokyo nationalised three islands in the chain, in what it said was a mere administrative change of ownership.