It happened at 9.26am today on the western side of the old crossing.
A witness said the boat, called Repertor and usually moored at Faversham Creek, appeared to have got its mast and rigging stuck on the lifting section of the bridge.
A tug tows the sailing barge Repertor off the old Kingsferry Bridge
The sailing barge which hit the bridge is normally moored at Faversham
The tug gets set to move the barge
The boat seen from the bridge. Picture: Ben Walledge
At about 10.20am, a Svitzer tug arrived to tow it free.
The top of the mast looks damaged.
The boat waits for the tug to tow it away
Network Rail engineers were called in to inspect the bridge.
It's understood services are beginning to return to normal.
A statement from train operator Southeastern said earlier this morning: "Train services running to and from these stations may be cancelled or delayed at short notice.
"An estimate for the resumption of normal services will be provided as soon as the problem has been fully assessed."
The statement said replacement bus services were in operation.
The bridge has not been closed to cars.
There are thought to have been about four people on board, who were not injured.