Burgess sustained the injury six seconds into the match but stayed on the field and won the Clive Churchill medal awarded to the game's outstanding player.
The 25-year-old, who moved to Australia in 2010, has signed a three-year contract with Bath and is hoping to break into the England team in time to play in next year's World Cup.
Burgess will undergo surgery on his cheekbone and is expected to be out of action for around six weeks.
(Reporting by Ed Osmond; editing by Justin Palmer)
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