The Eagles do not believe it to be a season-ending injury, but a source said Dillard will undergo further testing to determine whether surgery is needed and a timeline for return.
NFL Network was first to report the details of the injury.
Dillard, 26, serves as the primary backup to starting left tackle Jordan Mailata. Jack Driscoll is the top tackle option on the current 53-man roster. Philadelphia also has veteran Le'Raven Clark and Kayode Awosika on its practice squad.
Dillard was selected by the Eagles with the 22nd pick in the 2019 NFL draft and has started nine games for Philadelphia. He missed the 2020 season with a biceps injury. Dillard was also sidelined with a concussion for a portion of training camp but was coming off his strongest summer as a pro.