"We captured three today, including Abdullah Sonata. One was killed during an exchange of fire," the source from the police's anti-terrorism unit, Detachment 88, told the Reuters news agency.
The source said Sonata was found in possession of weapons.
Police in Indonesia had put him at the top of their most wanted list.
In the past year, Indonesian police have launched a nationwide crackdown on fighters, in which they have arrested or killed dozens of prominent fighters.
Linked to Noordin
Sonata was thought to have recently returned from the Philippines and started recruiting and training fighters.
He is linked to the late Noordin Mohammed Top,the former head of a Jemaah Islamiyah splinter cell known as "al-Qaeda in the Malay Archipelago", responsible for major bombings until he was killed last year by police.
Noordin had been accused of involvement in July's twin suicide bombings at the Marriott and Ritz-Carlton hotels in Jakarta, the 2002 Bali nightclub bombing and attacks on the same Marriott hotel in Jakarta in 2003, as well as the Australian Embassy in 2004.
Sonata was sought for his role in planning a training camp in Aceh region - on the northwestern tip of Sumatra island to the west of Java - and for recruiting new members.
Indonesia's Metro TV said police also discovered documents that showed fighters were planning to attack the Danish embassy in Jakarta, but the police source declined to confirm the report.
Denmark has been a frequent target in various countries following the publication in a Danish newspaper in 2005 of caricatures depicting the Prophet Muhammad.
In May, police said a group had set up a paramilitary training camp in Aceh and planned to launch a series of attacks.
These included a Mumbai-style hotel siege targeting foreigners and an assault on the president and foreign guests at an independence day ceremony in August.
Sonata had previously been arrested in 2004 for concealing information about Noordin, blamed for a string of bomb attacks against Western symbols over the past 10 years.
He was released in March 2009.