The extremists detained the fishermen after the vessel drifted into the militants' stronghold, Yasin Maalin, a resident of the town of El-Dher in Somalia's coastal region of Galgadud, told The Associated Press by telephone. Ali Hussein, another resident, corroborated his account.
Al-Shabab, a militant group that is allied with al-Qaida and has carried out many deadly attacks across Somalia, did not immediately claim the kidnapping.
On Wednesday night, the Iranian state television station's scrolling news bar announced the kidnapping, saying the vessel owned by an Iranian fishing organization suffered a technical fault near the Somali coast. It did not elaborate.
Despite losing some of its top leaders in U.S. airstrikes and being pushed by African Union forces out of the capital, Mogadishu, al-Shabab still has control over territory in south and central Somalia. The group carries out deadly bombings against government targets and public places seen as popular with foreigners.
The extremists also have attacked neighboring Kenya, which has sent troops to Somalia to fight the insurgents.
Piracy off the coast of Somalia once was a serious threat to the global shipping industry, but attacks have dropped dramatically the last several years after ships began carrying armed guards.