Jundullah has in recent years claimed responsibility for several bombing attacks inside Iran that have left dozens of people dead.
Television pictures showed Rigi being taken off the aeroplane in handcuffs, accompanied by four masked men.
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."
Speaking to Al Jazeera, Mahjoob Zweiri from Qatar University, said: "He [Rigi] was accused of being responsible of operations which basically annoyed the government in Iran.
"The Iranians look at him as a tool in different hands, sometimes in American hands, sometimes in Pakistani hands, sometimes in Israeli hands."
Soon after reports of Rigi's capture, Iranian media quoted Heidar Moslehi, 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," 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.
IRNA reported that Moslehi had blamed Dubai for being involved in Rigi's movements.
"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 agency quoted Moslehi as saying.
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 for the bombings last October 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.