Blyth, who joined the Sky Bet League Two side at the start of August on an initial month-long loan but recently saw the deal extended until November 2, sustained the injury in training on Friday.
The Cobblers are awaiting the results of a scan to determine the full extent of the damage but the early prognosis is that the 21-year-old will be absent for four weeks - taking him up to the end of his stay at Sixfields.
Northampton boss Aidy Boothroyd plans to contact Leicester to see if the loan deal can be rearranged in some way.
Speaking after his side's goalless home draw with Morecambe on Saturday, Boothroyd said: "We'll be talking to Leicester to see if we can do anything with it, maybe stop it and start it again.
"It will depend on the extent of his injury and we will be guided by them but hopefully he will be okay."