This is not the first time Kidney has had to cope without the Ulsterman, who also missed the opening game of last year's championship, but Leinster's Sean O'Brien has performed admirably in his place.
He said: "Stephen has been slow to recover and he will not be available for the Scottish game.
"He's seeing a surgeon in two weeks' time and the results of that consultation will determine his availability for the rest of the Six Nations.
"He's still a young but he's had problems with that knee before.
"I can't ever make any guarantees about any guys, I wouldn't second-guess that, there have been issues with it."
However Kidney has received a boost with the news last year's Six Nations Player of the Tournament Tommy Bowe is in contention for the Murrayfield trip, as are props John Hayes and Tony Buckley.
Ireland have had to make do without their Ospreys winger so far, with Leinster utility back Fergus McFadden impressing with a try in Ireland's narrow 25-22 defeat at home to France in the first championship game at the Aviva Stadium.
He added: "A lot of the guys are starting to come back. John is starting to run again and we'll see progress there at the end of this week. Tony is starting for Munster.
"There were no injuries arising from last week's game. Jamie Heaslip came through well without any reaction.
"Tommy is starting with the Ospreys in Italy and their physios are quite happy with his training. He's back into it and very comfortable running.
"So, there's no hassle for him playing - if he was showing discomfort, he'd have to be withdrawn.
"He's obviously a top player, but I'm more than happy with the way Fergus and Keith Earls have gone on the wings as well."