The Ghanaian had to be hauled off towards full-time after seemingly snapping his ankle during a challenge on Michail Antonio.
The match was the 23-year-old's ninth league appearance of the season, which is his seventh start.
"I hope it is not as a serious as we think. He will have to have an examination," Leicester boss Claude Puel said after the game.
"My first thought at the end is for my player Daniel.
"He played well and gave his best so it is difficult to see this injury at the end.
"He will have an exam and we will see after. He has gone to the hospital, of course.
"I thought more about that at the end than the game."
Fabian Balbuena opened the scoring in the 30th minute for visiting West Ham in Saturday's game, before Wilfred Ndidi netted a minute to full-time to restore parity.
He joined The Foxes in 2016, making five appearances as the club won the 2015-16 league title.