Kante has proved to be one of the bargains of the season since joining from Caen for a measly £5.6million in August, playing an integral part in helping the Foxes defy the odds by reaching the Premier League summit.
The 24-year-old was withdrawn in the 70th minute of Saturday's last-gasp 1-0 victory over Norwich and manager Ranieri expects the Frenchman to miss Leicester's upcoming matches against West Brom on Tuesday and Watford on Saturday.
"N'Golo Kante I think we'll lose for the next two matches," Ranieri said at a news conference ahead of his side's clash against West Brom at the King Power Stadium tomorrow.
"He has a little pain with his hamstring so I need to give him some rest."
The Italian is confident Andy King, who replaced Kante against Norwich, can step up in his team-mate's absence.
RUMOURS | Arsenal join Mahrez race
"We put King on and he plays very well with [Danny] Drinkwater. I'm very confident in him," he added.
Leicester needed an 89th-minute winner from Leonardo Ulloa to down a dogged Norwich outfit at the weekend and keep their place at the top of the table.
The Canaries caused Ranieri's men plenty of problems with their rigid structure and the Itaiian says he expects another tough game when his side play hosts to West Brom.
"We have to be patient and find a solution. The first match against West Brom was very difficult and they scored first," he said.
"Everybody knows us and we have to continue with our football, be intelligent and wait for the right moments.
"We know they counter well and are very dangerous at corners. They scored eight or nine goals from set plays. They are very dangerous."