Williams sprained an ankle late in a 26-17 victory over the Seattle Seahawks on Thursday. He will miss a minimum of three weeks.
Rams coach Sean McVay said the team was working through the process of figuring out who would replace Williams, who has 29 tackles and 2 pass deflections in five starts.
"It might not be one guy," McVay said. "It might be kind of by committee approach."
The Rams have consistently started three cornerbacks this season under first-year coordinator Raheem Morris, and with the exception of starters Williams and Jalen Ramsey, the trio has recently been in flux.
McVay said in going forward without Williams that all possibilities, including different personnel groupings and the number of corners playing, would be explored.
The Rams are 4-1 and in second place in the NFC West as they prepare to travel to New York to play the 1-4 Giants on Sunday.