The announcement came hours after the pirates and naval forces exchanged gunfire over a boat believed to be carrying supplies to the hijackers.
The tanker, which was en route from Djibouti to the Somali capital, Mogadishu, was seized on Monday with eight Sri Lankan crew members on board.
It is the first hijack off Somalia's coast since 2012.
Abdirahman Mohamud Hassan, the director general of the Puntland maritime police force, said: "There has been discussion going on after the gunfight this afternoon... We took our forces back and thus the pirates went away."
The Sri Lankan foreign ministry said the crew members were released "unharmed, without the payment of a ransom".
A pirate confirmed the release was made without a ransom payment, according to Reuters.
However, John Steed, a former British army officer who has spent years negotiating the release of piracy hostages in Somalia, told the AFP news agency they had been made an offer they could not refuse.
Mr Hassan earlier said that "pirates" on board the tanker had opened fire on Thursday after authorities tried to intercept a boat believed to be carrying essential supplies, such as food.
Four people were wounded in the exchange of fire on Thursday, the BBC has learned.
The Puntland authorities deployed local forces in the area in an attempt to assist rescue efforts for the hostages on board the vessel, the district commissioner said.
The vessel was carrying oil and was owned by the United Arab Emirates (UAE), despite conflicting reports over the flag it was sailing under, he added.
On Wednesday, the European Union anti-piracy naval force, which is helping to tackle piracy in the region, said the hijackers had been demanding a ransom.
Authorities were then still trying to determine whether the gunmen, who have not given any details about the size of the ransom, were organised pirates or fishermen whose equipment was destroyed by illegal fishing vessels, as they had claimed to be.
The EU force earlier made contact with the ship's master, who said his vessel and crew were being held captive anchored off the coast of north-east Somalia. The ship's tracking system has reportedly been switched off.
Piracy off the coast of Somalia, usually for ransom, has reduced significantly in recent years, in part because of extensive international military patrols as well as support for local fishing communities.
At the height of the crisis in 2011, there were 237 attacks and the annual cost of piracy was estimated to be up to $8bn (Â£7bn).
However, some smaller fishing vessels have recently been seized in the area.
In 2015, Somali officials warned that piracy could return unless the international community helped create jobs and security ashore, as well as combating illegal fishing at sea.
Some Somali fishermen turned to piracy after their livelihoods were destroyed by illegal fishing from foreign trawlers, which benefited from the lack of a functioning coastguard in the country following years of conflict.
Somali pirates who hijacked an oil tanker have released it without condition, according to officials.