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.
Hundreds of police officers have begun an operation to arrest a trade union leader who has taken refuge in a Buddhist temple in Seoul.