The 22-year-old came off 70 minutes into Saturday's 3-2 League Two defeat by Shrewsbury.
"It was disappointing because you don't want to be losing your better players," Cobblers boss Gary Johnson told the club website.
"He's suffered a dislocation so he is going to be out for a few weeks and we wish him a speedy recovery."
McKay, who arrived at Sixfields from Leicester in the summer of 2009, has scored eight times in 38 games this season.
Johnson bolstered his squad on Monday with the loan signings of Wolves left-back Jamie Reckord and Peterborough pair Steve Collis and Seth Nana Ofori-Twumasi.
Source: BBC Sport
Source: BBC Sport