The injury, which could keep him out as long as two months, will not require surgery, the source said.
"Typically, it would take 6 to 8 weeks recovery, but [his] injury is so that he could be back 4 to 5 weeks," the source said, leaving the door open for Vea's possible return as early as the regular-season opener against San Francisco on Sept. 8.
Vea suffered the injury during blocking drills in Tuesday's practice. He was able to walk off the field without assistance but underwent an MRI that night. Due to swelling and fluid in his knee, they wanted to repeat testing, head coach Bruce Arians said.
The Bucs' 12th overall draft pick in 2018, Vea missed all of training camp and the first three games of the season last year due to a strained calf muscle, but he finished the season with 3.0 sacks and was having a promising training camp playing alongside Ndamukong Suh.
The Bucs' defense is already without star pass-rusher Jason Pierre-Paul, who suffered a neck fracture in a car accident this offseason.
ESPN's Adam Schefter contributed to this report.