Williams appeared to injure his leg after he was beaten on a pass by wide receiver Mike Williams, according to multiple media reports.
The incident comes four days after former Pro Bowl cornerback Jason Verrett suffered a season-ending torn Achilles during a conditioning test on Friday.
Signed as an undrafted free agent out of Penn State by the Chargers in 2016, Trevor Williams started five of 12 games during his rookie season, registering 23 tackles and five passes defensed.
With Verrett limited to four games last season, Williams started 15 games and had a pair of interceptions, 21 passes defensed and 54 tackles.
If Williams is out any amount of time, Desmond King likely will take his place. King had an interception and 4.0 sacks while starting four of 16 games as a rookie in 2017.