Coast guard Capt. Jim Chmiel said the ship was being towed to a location in the mouth of a sheltered harbour by a coast guard rescue boat at 9 p.m. local time.
He said pumps were working well and the ship — which was moving navigation buoys when it hit the shoal — is not in danger of sinking.
No injuries were reported among the 26 crew members and two cadets who were on board and the coast guard says in a statement that all personnel were safe.
Chmiel, the superintendent of the coast guard's regional operations centre, had said earlier the ship planned to remove as many as four non-essential crew members from the Ann Harvey.
He said the ship's captain later decided to limit the evacuation to the two cadets.
Chmiel said the Canadian Coast Guard Ship Louis S. St-Laurent was expected to arrive early Thursday to take over the towing of the damaged vessel to the sheltered location on the southwest coast where it will remain at anchor.
The ship took on water in the propulsion motor room and two electrical motors are damaged, he said. Pumps were keeping up with the flow of water coming into the damaged compartments and Chmiel said the situation was "stabilized" by early Wednesday evening.
"The water is not rising any more and the (pumps) are keeping up to the inflow of water," he said.
There was no marine pollution from the incident, said Chmiel.
A team of navy divers were being flown to Burgeo, N.L., and were expected to come aboard the coast guard vessel late Wednesday or early Thursday morning to examine the damage.
The coast guard said it is co-ordinating its efforts with the military's Joint Rescue Co-ordination Centre in Halifax.
Once the Louis S. St-Laurent arrives, it will be on standby until another ship, the Teleost, arrives around noon on Thursday to assist in a towing operation back to St. John's.
The coast guard said the weather in the area is good, with northwest winds forecast to be 35 kilometres per hour overnight. It says the winds are favourable to the ship's position.
The Ann Harvey was built in Halifax in 1987 and can carry 47 people.
In addition to having ice-breaking duties, the diesel-electric ship is used to tend buoys, in search and rescue operations, fisheries enforcement and the construction of marine navigational services. Its hangar can house two helicopters.
— By Michael Tutton in Halifax.