Williams, who played at San Diego's Rancho Bernardo High, came out of Thursday night's game after just 3 2/3 innings.
To take his roster spot, right-hander Clay Holmes was recalled from Triple-A Indianapolis on Friday. It's Holmes' second stint with the Pirates this season.
The Pirates also optioned right-hander Richard Rodriguez to Triple-A and selected the contract of right-hander Geoff Hartlieb from Indianapolis. Hartlieb has no previous big league experience.
Additionally, catcher Jacob Stallings cleared outright waivers and was assigned to Indianapolis.