"Rigi was arrested in Persian Gulf waters while he was travelling on a plane via Pakistan to an Arab country," Mohammad Dehghan was quoted Iran's the official IRNA news agency as saying.
"His plane was ordered to land, and then he was arrested after the plane was searched."
Television pictures showed Rigi being taken off a aeroplane in handcuffs, accompanied by four masked men.
Al-Alam television, the state-owned Arabic language service, reported that Rigi was arrested "inside Iran", in the eastern part of the country, prompting speculation that Iran might have intercepted Rigis aircraft and forced it to land in Iran.
Alireza Ronaghi, Al Jazeera's correspondent in Tehran, said Rigi was a key target for Iranian intelligence.
"He [Rigi] has never denied that his group has some drug trafficking as his main economic backbone and Iran accuses him and his group as having the backing of American forces in the region and having a clear relationship with American intelligence," he said.
"Iran's interior minster says it has been very important for Iranian intelligence agents to arrest him alive."
Soon after reports of Rigi's capture, Iranian media reported Iran's intelligence minister as saying that Rigi had spent time at an American military base prior to his arrest.
"Abdulmalik Rigi was in an American military base 24 hours before his arrest ... He also travelled to some European countries ahead of his arrest," Heidar Moslehi was reported by Iran's Press TV as saying.
Moslehi was also quoted as saying that the Americans had issued Rigi with "an Afghan passport and an identification card for travelling to Pakistan" and that Rigi was in league with British and Israeli intelligence.
The official IRNA news agency quoted Moslehi as saying: "Dubai has a smeared hand in this scandal that shows the Zionist regime wants to turn the region into a safe haven for terrorists with the help of America and Europe."
The "Arab country" Rigi was reportedly travelling to is thought to have been Dubai.
The US, Britain and Pakistan all deny backing Jundullah, which operates in Iran's southeastern province of Sistan-Baluchistan, bordering Pakistan and Afghanistan.
The group, which Iran suspects of having links with the al-Qaeda network, gained prominence six years ago with a series of sporadic attacks and kidnappings.
It claimed responsibility last year for an October 18 bombing that killed more than 40 Iranians, including 15 from the elite Revolutionary Guards.
Jundullah accuses the government of discrimination against Sunnis and says that the minority Sunni tribes in southeastern Iran suffer at the hands of Tehran's Shia leadership, an allegation Tehran rejects.
Sectarian violence is relatively rare in Iran, but attacks and clashes have increased between security forces, Sunni rebels and drug traffickers in the country's southeast.