The Arsenal academy graduate picked up the problem earlier this month in the 3-1 defeat at Manchester United.
The 22-year-old has been restricted to four substitute appearances in the Premier League this season.
Last term, Smith-Rowe enjoyed a massive breakthrough with the Gunners, scoring 10 goals in 33 Premier League appearances and earning a call up to Gareth Southgate's England squad.
But Smith-Rowe is highly unlikely to be part of England's traveling party to Qatar in November, with his temporary lay off expected to last for more than two months.
"In recent months, Emile Smith Rowe has been experiencing discomfort in his groin, which has limited his training and match appearances," Arsenal announced in a club statement.
"Following a significant setback at our Premier League match against Manchester United at Old Trafford on September 4, and after further specialist consultations and discussions with our medical team, Emile underwent surgery to repair a damaged tendon in his groin.
"This successful surgery took place in London in the past few days and Emile’s rehabilitation programme is already under way. We are hopeful that Emile will return to full training in December.
"Everyone at the club will now be supporting and working hard with Emile to get him back on the pitch as soon as possible."
Table-topping Arsenal will host North London rivals Tottenham Hotspurs in the Premier League this weekend.
