The Colorado Rapids striker has had surgery on his leg after he was taken off on a stretcher in the Dublin game.
"Thanks to plastic surgeons at the Mater Hospital, leg looks brand new," said the 32-year-old on Twitter.
Doyle, Daryl Murphy, Robbie Keane and Jon Walters will all miss Tuesday's game against Slovakia in Dublin.
Former Wolves and Reading striker Doyle looked in danger of missing out on Euro 2016 as he was left writhing on the ground in Friday's game after making a block tackle.
However, the striker allayed those fears on Saturday morning, saying he aimed to be "back jogging in a few weeks" after earlier tweeting a picture of his leg.
Keane was ruled out of Friday's win over the Swiss and manager Martin O'Neill said after the game that the squad captain is now "a wee bit concerned about the injury".
"It's something he thought was a kick for a start, he thought it would clear up in a couple of days," said the Republic boss.
"He will miss Tuesday's game definitely now. I am hoping that's not a major concern at the moment and I genuinely don't think it is, so I don't want to start a bit of scaremongering."
Stoke striker Walters will again miss Tuesday's game as he continues to be bothered by a hamstring injury while Daryl Murphy, who replaced Doyle on Friday, has returned to his club Ipswich Town because of a calf strain.
With Doyle's injury not as serious as first feared, O'Neill was reasonably content with a night's work which saw him running the rule over a number of fringe players.
With Shane Duffy impressing in central defence, Shane Long hit the woodwork although the visitors missed late chances with Republic keeper Darren Randolph saving a deflected Granit Xhaka shot.
"We probably lacked a little bit of cohesion, but it was nice to keep the momentum going against what I thought was a very fine Swiss side," said O'Neill.

Scientists from Stirling University looked at the effects a group of beavers had on a wetland in Tayside originally drained for farming.
The 12-year study found plant richness rose by 46% and the number of different plants recorded more than doubled.
The study is the first to measure the environmental benefits of the beavers' activity over time.
Between 2003 and 2015, the beavers constructed 195 metres of dams, 500 metres of canals and an acre of ponds at the site on a private estate in Blairgowrie, Perthshire.
Scientists said the surrounding vegetation "increased in complexity" by 71%.
Prof Nigel Willby from the university said wetlands were "tremendously important environments" for biodiversity, but were disappearing at an "alarming rate".
He said: "Beavers are renowned for their engineering skills, like dam building, and are now being considered as tools for restoring wetlands.
"They have been reintroduced widely, including in Scotland, partly for this purpose and our findings demonstrate the surprisingly large benefits they can bring to biodiversity."
The study was partly-funded by Scottish Natural Heritage (SNH) and published in the international journal Science of the Total Environment.
Following trial reintroductions, Eurasian beavers were readmitted to Scotland last year, 400 years after being hunted to extinction in the UK.
Co-author Dr Alan Law said: "We know lots about the benefits of beavers in natural settings, but until now we did not know the full extent of what they can achieve in present-day landscapes where restoration is most needed.
"Seeing what beavers can do for our wetlands and countryside highlights the diverse landscape we have been missing for the last 400 years."
Republic of Ireland striker Kevin Doyle said there was "no major damage" after suffering a deep leg gash in Friday's 1-0 win over Switzerland.
[NEXT_CONCEPT]
A new study has highlighted beavers "exceptional" ability to rebuild diverse wetlands.