The gang is also wanted in several cases in other cities, they said.
Joint Commissioner, East (Law and Order), S Manoharan said special teams were formed to nab the gang following a spate of chain snatching incidents in the city.
Their modus operandi was to arrive in Chennai by flight, purchase used motorcycles by producing fake documents and then target women in isolated areas or places which do not have surveillance cameras, he told reporters.
They were arrested after police scanned CCTV footage from a bakery shop, he said, adding that gold jewellery was recovered from them
The commissioner said another special team was now in New Delhi to nab the other three gang members.