The attack holed the Japanese tanker, causing it to leak hundreds of gallons of fuel on Monday. No one was injured.
Yacht seized
The pirates on the Spanish boat are thought to be now sailing it to the Somali coast.
"I am the captain of the boat ... we are all well and there is no problem, for the moment there is no problem," the skipper said in Spanish, before being interrupted by the pirate who said he was a member of a "Somalia militia", a government source said earlier.
The fishing vessel, Playa de Bakio, had 13 Spanish nationals and 13 foreign crew members on board.
Spain's foreign ministry said no one was injured in the attack, which was apparently carried out by four pirates using grenade launchers.
The seizure came two days after a Paris court charged six Somalis with taking the crew of a French yacht hostage earlier this month.
The six were captured by French special forces, along with $200,000 of suspected ransom money, after they released the 30-strong crew of the yacht on April 11.
They had held the group for a week.
The coastal waters of Somalia, which has not had an effective central government for more than 17 years, are considered to be among the most hazardous in the world.
Last year more than 25 ships were seized by pirates in Somali coastal waters despite US navy patrols.