He is not expected to miss any regular-season games, the source said.
"It was better than we thought," said coach Dirk Koetter, who initially feared that it was a torn Achilles.
Vea was able to gingerly limp off the practice field Sunday, but he had to be carted to the locker room. The injury happened on a run play during 11-on-11 drills.
"What Vita described when it happened was what you would think if a guy tore his Achilles, which would be year-long injury," Koetter said. "Thankfully it was not that. It's a calf injury. He's going to be out for right now, but it's not what it could have been. So in that respect, we're better off than we thought we were."
Vea was in a walking boot and riding a scooter on the sideline during Tuesday's practice. He spent the majority of practice off the leg but was able to put some weight on it as he left the practice field.
The 12th overall draft pick in the 2018 NFL draft, Vea is expected to step in and start alongside Pro Bowl defensive tackle Gerald McCoy. With him out, the Bucs will rely on Beau Allen, whom they signed as an undrafted free agent out of Philadelphia this offseason.