Amartey sustained an injury during Sunday's 3-0 Premier League defeat to West Ham United at the King Power stadium.
In his third competitive game since returning from a two-year lay-off, the Ghanaian defender was substituted in the 55th minute of the matchweek four fixture after appearing to have picked up an injury.
"It looks like his hamstring, but we’ll get confirmation in the next couple of days," Rodgers said after the game, as reported by his club's official website.
"I felt that from the first whistle – we had some good moments in the first half – defensively, we weren’t aggressive enough. I said to the players at half-time that we needed to get into contention," Rodgers added.
"We’re about aggression and getting up to people, especially when they defend deep and their game plan is to break up our pressure. You have to be really good on the counter-press and we were nowhere near it in that aspect.
"That gave them opportunities to break out. We still had good moments in the first half where we played through them, we just lacked the quality in the final pass to make it count.”
The latest injury will be a massive setback for Amartey who was hoping to regain full match fitness with a run of games and cement a permanent place in the Leicester set-up after a two-year absence.