The 36-year-old Cardiff Blues loose-head prop, who captained Wales in their 27-13 win over South Africa in November, has ruptured a bicep muscle.
Blues head coach Danny Wilson confirmed Jenkins underwent surgery on the injury on Tuesday.
"It's a big blow for us, it's a big blow for Wales," said Wilson.
If Jenkins is back in three months he will return before the end of Wales' Six Nations campaign, which begins against Italy in Rome on Sunday, 5 February and ends on Saturday, 18 March against France in Paris
Wilson is hopeful Jenkins can battle back to fitness earlier than forecast.
"Knowing Gethin he'll get back before three months," said Wilson.
"He's one of the most professional men in terms of rehab that I've come across, looking after his body, so whatever he's asked to get that right, I know he'll do it."
Jenkins - who has played 129 times for Wales - captained Rob Howley's team in the autumn internationals against Australia, Argentina and South Africa.
"I think the form that he's been in, he's proving to people that age is just a number because he certainly looks after himself better than most," added Wilson.
"His performances for Cardiff Blues and Wales have been of a real high standard."
The Blues captain and will be absent when they host Bath in the European Challenge Cup on Thursday, followed by their Pro12 festive derbies against Newport Gwent Dragons and Scarlets.
Wales prop Gethin Jenkins has been ruled out for at least three months and is in danger of missing all of the 2017 Six Nations.