The 37-year-old flanker is suspected of running away from a taxi without paying roughly 10,000 yen (US$90) for the fare near his home in the small hours of December 31, according to Tokyo Metropolitan Police.
The driver chased Smith, who then allegedly punched the driver in his face, causing "injuries that require two weeks to fully heal," police spokesman Naoto Wakabayashi told AFP.
Smith, who is now playing for Japan's Suntory Sungoliath team, was drunk at the time and was arrested on the spot by a police officer, the spokesman said.
He denies the allegations, but is still in police custody, Wakabayashi said.
Smith, who won 111 caps, is seen as a Wallaby great and twice won the prestigious John Eales Medal for best Australian rugby player.
"We sincerely apologise to the victim and other parties concerned. We are also sorry for causing concern and trouble to many people in the public," Suntory said.
Suntory officials said they were not aware of further details about the case.
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