"We can confirm that there has been a breach of team discipline. This is being dealt with within the squad," an SFA spokesman said on Wednesday.
He was reacting to media reports that the Rangers pair had stayed up drinking after Scotland's 3-0 defeat by the Netherlands in Amsterdam on Saturday.
"We are not allowing this to disrupt preparations for tonight's vital World Cup qualifying match."
The SFA earlier told the BBC Ferguson and McGregor, who made his first start in a competitive game against the Dutch, would remain with the squad for the match.
"Due to a breach of team discipline, they will not play," an FA spokesman was quoted as saying. "However, they could still join the squad at Hampden for the match."
It is a damaging blow for Scotland manager George Burley, whose side were beaten 3-0 by the Netherlands in Group Nine on Saturday and who need to beat Iceland at Hampden Park to maintain their hopes of finishing runners-up in the group.
The Scots, who are level on four points with second-placed Iceland and eight points behind group leaders Netherlands, are already without several experienced players because of injury.
Craig Gordon, who was replaced by McGregor in Amsterdam, is expected to return against Iceland with defender Stephen McManus, who missed the defeat in Amsterdam through injury, wearing the captain's armband.
‘I don’t think Liverpool would look at Ollie Watkins, a striker isn’t a pressing issue for them – it’s Arsenal who need one’ Former Reds star explains why his old club don’t need an out-and-out forward this summer
‘He’ll still be playing at 40 at a good level because he’s in such good shape and looks after himself so well. He does everything to be a top professional’: Ex-Liverpool coach insists Mohamed Salah has plenty more miles in the tank
