The 27-year-old suffered the injury in a clash of heads with Josh van der Flier during Cardiff Blues' 13-16 defeat by Leinster on Saturday.
Warburton will have a small plate inserted in his face. The Blues say he will be out for two to four weeks.
Wales play Australia, Argentina, Japan and South Africa in November.
"It's disappointing for Sam," said Blues backs coach Matt Sherratt.
"He was getting a run of games and getting into some form, so I'm disappointed for him.
"It's not too serious and as far as the Blues are concerned it's chance for someone else to come in and start some games."
Sherratt will be part of Rob Howley's Wales coaching team this season.
Warburton's injury is believed to be similar to one suffered by Dan Lydiate during the 2016 World Cup.
The Ospreys flanker missed only one match - the 15-6 loss to Australia - before returning to play in the quarter final against South Africa.
However, the surgery adds to a back row injury headache for Howley, who is in the Wales role while head coach Warren Gatland takes charge of the British and Irish Lions.
Lydiate has not played yet this season after undergoing surgery on a shoulder in June, while number eight Taulupe Faletau has been out since injuring knee ligaments on his Premiership debut for Bath on 3 September.
Wales captain Sam Warburton will have surgery on a fractured cheekbone and faces a race to be fit for the Test against Australia on 5 November.