Konchesky was replaced at half-time during the Foxes' 1-1 home draw against Leeds on Tuesday night after complaining of tightness in his hamstring.
The experienced left-back underwent a scan on Wednesday and manager Nigel Pearson hopes they have caught the problem early enough.
"His hamstring was tight and it has been scanned. Hopefully we have got it in time," Pearson told reporters ahead of Sheffield Wednesday's visit to the King Power Stadium on Saturday.
"He has been a very consistent player for us so, hopefully, it will not be too big a problem. But we have to wait to see the results of the scan."