Marpet left Sunday's game against the Atlanta Falcons with a knee injury after getting rolled up on and did not return.
Dotson also suffered a knee injury but did return to the Sunday's game. He told ESPN on Wednesday that he tore his posterior cruciate ligament.
"As far as Ali goes, I think he played his best football the last two weeks of the season," Bucs coach Dirk Koetter said. "As far as Demar Dotson goes, I think Dot -- in my three seasons here -- had his best season overall. I think Dot was holding down the right tackle spot well, especially in pass protection. It's disappointing that you take two guys that are playing well on a team that needs more consistent play and they are out, but that is the worst part of this game and something that is uncontrollable [are] injuries.
"To my knowledge, those are both in the six-to-eight-week category injuries that would not require surgery. I am not a doctor, but that is what I've been led to believe."
Sunday's injuries depleted a Tampa Bay offensive line that was already missing left guard Evan Smith due to a concussion.
The Buccaneers are now in a challenging situation because starting quarterback Jameis Winston was cleared Monday to resume throwing after suffering a sprained AC joint in his throwing shoulder -- an injury that forced him to miss three games.
The expectation was that, if all went according to plan, Winston would start this week against the Green Bay Packers. But his injury, the result of a hard hit from Chandler Jones in Week 6, could be worsened by a hard blow.
The Bucs have promoted tight end Alan Cross, defensive end Patrick O'Connor and as previously reported by ESPN, wide receiver Jesus "Bobo" Wilson from the practice squad, and signed cornerback Deji Olatoye to the active roster. The Bucs also waived veteran tight end Luke Stocker and defensive end Darryl Tapp on Tuesday.