Hawkins, 24, had surgery on Friday and he is set to go on the injured reserve list, a source said.
After practice, several teammates expressed the difficulty of a teammate going down in mid-practice.
"Crappy thing," quarterback Landry Jones said.
Hawkins, a fourth-round pick in 2016, primarily backs up left tackle Alejandro Villanueva and played in five games with one start last season.
This was a big offseason for him to create a steady role along the offensive line. The Steelers drafted tackle Chukwuma Okorafor in the third round in last month's draft.