Puneet was arrested on Friday and was sent to judicial custody after he was produced before a judicial magistrate on Saturday, Banur police station SHO Bikramjit Singh Brar said.
"We have informed the Australian High Commission about the arrest," said Brar.
Puneet fled Australia in 2009 after he was convicted in a hit-and-run case in Southbank, in which a 19-year-old youth was killed and his friend injured.
He fled the country without serving the sentence on a passport he obtained from a friend who was later jailed for "perverting the course of justice".
Indian police too published advertisements in local newspapers urging people to come forward with information on his whereabouts.
The 24-year-old, now lodged at the Patiala central jail, will face an extradition hearing.