The defender had been struggling with a knock since the Jags' win over Hearts earlier this year and had an operation last week after discussions with manager Alan Archibald and Firhill physio Kenny Crichton.
Muirhead is likely to be sidelined for at least four weeks, but could face as much as six weeks out of action.
As revealed in SportTimes last week, boss Archibald has a defensive crisis on his hands with Stephen O'Donnell ruled out for the rest of the campaign with a hip knock.
It is touch and go whether Muirhead will recover in time to play again this term but the 23-year-old will give it his best shot as the battle to beat the top-flight drop intensifies.
"It's obviously very frustrating missing out," he said.
"We have a tough run in and everybody knows what's expected of us - I just wanted to be part of that.
"I'm completely focussed on helping the team out so it's disappointing not to be involved.
"However I'm feeling fit now and, if I work hard, I can hopefully get back involved before the end of the season.
"The knee is still quite achy but that obviously comes part and parcel with having an operation.
"Unfortunately it's just one of those things and I'll hopefully be back training sooner rather than later."
Thistle had hoped to postpone Muirhead's surgery until the end of the season but the Jags must now sweat it out to discover when he will be fit to return to action.
He could be back running as early as next week fitness guru Crichton puts him through his paces.
And the defender is prepared to put in the hours to ensure his recovery goes as smoothly as possible.
MUIRHEAD said: "As far as I know the operation went well, it wasn't anything too major and I think it went as much to plan as any operation can.
"Kenny has already given me a list of things to be working on and we can gradually build it up from there until I'm back training.
"I can feel the benefits of the work we're doing already. Obviously I'm not 100% but I've already got some movement back which is much quicker than I was expecting.
"It's all gym work just now and I'm mainly focussed on building the thigh muscle back up, as the muscle wastes away quite quickly when you aren't using it all the time.
"Once that's strengthened a bit and the pain has gone I'll get back to doing some light running and we'll see how we go from there.
"I've already been on the cross trainer a fair bit so hopefully I won't be too far away from doing some jogging."
While Muirhead has not given up hope of pulling on a red and yellow shirt again this term, he is definitely out of Thistle's first post-split fixture against Killie this weekend.
Archibald's side face a huge few weeks as they battle it out with four other clubs to avoid the Premiership play-off place and retain their top-flight status for next season.
And the Jags star insists he won't rush himself on the road to recovery.
"I've never had an operation before so I don't really know about recuperation time or anything - even if I did I'm not sure I'd be setting targets," Muirhead told ptfc.co.uk
"I'll just leave it in the hands of Kenny and the doc and see how we go from there.
"For me it's better to take it one step at a time and recover properly rather than rushing back only to break down again further down the line."