Authorities say the man orchestrated clashes with police during a large protest in Seoul on 14 November.
Han Sang-gyun, head of the Korean Confederation of Trade Unions has been in the temple ever since the protest.
Monks earlier warned police not to force their way inside, saying it would be a breach of their religious rights.
In the early evening, shortly after a deadline passed to give himself up, police sealed off the Jogye Temple in central Seoul and began the operation to arrest Mr Han.
Those at the protest in November had a diverse range of grievances, from President Park Geun-hye's business-friendly economic policies, to a decision to force the nation's schools to only use state-approved history textbooks.
The rally saw clashes between police using pepper spray and water cannon, and protesters, some of whom were armed with metal pipes and sharpened bamboo sticks.
The unforgiving police response prompted a smaller demonstration on Saturday - 14,000 people, rather than the 60,000 estimated at November's rally - to demand an apology from the president.
Ms Park had drawn the ire of labour unions and farmers for planning to make it easier to dismiss workers and to cap the salaries of senior employees. However, many of her labour market policies are more popular with the general public, according to polls.
The BBC's Stephen Evans in Seoul says there is an increasingly bitter division between South Korea's right of centre government and its left-wing critics, who accuse it of diminishing democracy.

Manas Kongpan is among more than 60 people convicted in Bangkok of trafficking Bangladeshis and Rohingya Muslims, a minority fleeing Myanmar.
Another top former official was sentenced to 75 years in prison. More than 100 defendants were on trial.
Muslim Rohingya have been fleeing Myanmar for years, paying people smugglers to help them escape.
The arrest of the general in June 2015 was seen as part of an effort by Thailand to close down a human smuggling route through the country.
The judge found him guilty of human trafficking and organised transnational crime.
A former head of administration in the southern province of Satun, Ko-Tong (also known as Patjuban Aungkachotephan), received a sentence of 75 years in prison.
Several other defendants were handed jail terms of similar length. Sentences ranged from four to 94 years.
In 2009, Manas told the BBC that Thailand treated migrants humanely after he was accused of ordering more than 1,000 Rohingyas to be set adrift at sea on boats with no engines.
Correspondents say he is the first member of the military in army-ruled Thailand to be implicated in the trafficking of migrants.
Prime Minister Prayuth Chan-ocha, head of the country's ruling junta, urged the public not to blame trafficking on military figures.
"There are many people in this human trafficking network," he told reporters. "Don't group all soldiers in the country as one."
In 2015, thousands of refugees were left stranded at sea as they tried to escape through southern Thailand and on to Malaysia and other destinations.
The crisis escalated after international pressure forced the Thai authorities to crack down on the smuggling networks.
This led to the smugglers abandoning the refugees, leaving them on their sea and land routes with no neighbouring country willing to take them in.
The current trial was sparked by the discovery of mass graves of refugees in jungle camps near the Thai-Malaysian border.
Most of those indicted are from Thailand but several citizens of Myanmar (also called Burma) and Bangladesh are also being held.
A senior policeman who led an investigation into human trafficking in Thailand, Major General Paween Pongsirin, fled to Australia fearing his life was in danger from influential figures implicated in trafficking in his country.
The Rohingya - a distinct Muslim ethnic group who are effectively stateless - have been fleeing Myanmar for decades with Thailand, Malaysia and Indonesia the most desired destinations.
While they say they are descendants of Arab traders who have been in the region for generations, Myanmar's government insists they are not a genuine ethnic group but rather Bengali migrants.
Among the refugees stranded during the 2015 crisis were also many economic migrants from neighbouring Bangladesh.
Hundreds of police officers have begun an operation to arrest a trade union leader who has taken refuge in a Buddhist temple in Seoul.
[NEXT_CONCEPT]
A former Thai general has been sentenced to 27 years in jail for human trafficking at a landmark trial.