The Croat midfielder ruptured his cruciate ligament last month in a freak training ground accident.
The devastating injury means the former Portsmouth, Tottenham and QPR attacker will not feature again this season.
Warburton has cautioned supporters with the news that the 32-year-old is for a long battle, but he i s hopeful Kranjcar will make a full recovery
The Englishman told Gers' official website: "Niko's operation went well, the stitches came out on Monday, which he is pleased about and the inflammation is down
"He is going through the normal four weeks [recovery period] and then after four weeks he will revisit the surgeon and hopefully get the green light to push on from there.
"It is a really structured week-by-week programme, there is no cutting corners and unfortunately it is a very common injury in football now but the programme is set.
"It is a week-by-week programme and you can't be doing well at four weeks and jump ahead to eight, it doesn't work that way, you have to go step after step.
"He is in great hands and his attitude is first class and we have no doubt he will return back fitter and stronger than ever."
Warburton has also been left frustrated after seeing promising midfielder Jordan Rossiter suffer another a set-back in his fight for fitness
The 19-year-old Liverpudlian is nursing a calf injury, having not played since late August when he hobbled off against Kilmarnock.
"Jordan is getting there, he had a small set-back and there is a lot of work being done with him," said Warburton
"Jordan is a boy who just wants to play football
His ability is more than evident to anyone who has seen him play this season.
"The frustration is obvious, but he's working hard and these things happen, these frustrations come with the game.
"Jordan is very frustrated at the moment, but there is no doubt his quality is there and we'll see it sooner rather than later I'm sure."
Meanwhile, Warburton has sent first-teamers Philippe Senderos, Danny Wilson, Matt Crooks, Martyn Waghorn and Barrie McKay north with the Light Blues Under-20s side for Tuesday's development league clash with Ross County
Centre-backs Senderos and Wilson are making their way back from injury and Warburton wants the rest of the group to pick up some valuable action ahead of Saturday's Ibrox clash with Dundee
Warburton said: "We had a decent session on Monday and four or five of the boys will be involved in the Under-20s game on Tuesday at Ross County.
"That is good for them and means they can get some pitch time after the break, that has worked out well for us and they have a good playing surface up there.
"We will probably look to involve Philippe and Danny from a defensive point of view, Matt Crooks and Barrie McKay will get some pitch time and Waggy will play too.
"Waggy, all credit to him, was keen to play in the last 20s game, but it was an artificial surface and we were hesitant.
"They are putting four or five first-teamers out as well, so hopefully it will be a good test and they will look forward to that.
"We were down to two centre-halves and all credit to the medical and performance guys for working so hard and to the boys for putting the effort in.
"They boys are back and training with us and they need minutes now, at the moment Clint and Rob have the jerseys but it is about being ready when your chance comes along."
Source : PA