The Irish defender had to go off early in the second-half at Bootham Crescent after a strong challenge from a home defender, and the club predicted three weeks on the sidelines.
Although that means he is now likely to miss the game at Reading on Saturday August 7, he was already expected to miss the Carling Cup tie at home to Oldham Athletic three days later as he was due to join the Republic of Ireland U21 squad for a European Championship qualifier.
His participation in that match must now be in doubt. Nolan's injury was the low point of Tuesday's defeat at the Minstermen, a match manager Nigel Adkins and the 142 Iron fans who made the trip would be keen to forget.
"As I've said throughout pre-season, it's not about the result but the performance we're looking for. It was a tough second half, and it is fair to say they had a couple of opportunities before their goal," Adkins told United's official website.
"All in all, it was a good lesson for some of the younger players and certainly a lesson for ourselves in seeing if some of the younger players can step up to the mark."