The news was first reported by NFL Network.
The two-time Pro Bowler left Sunday's game against Arizona in the second quarter and did not return. He suffered the injury while coming out of the backfield, taking a pitch to his right. He made a cut and planted his foot, which is when he felt the pain in his right hamstring. He grabbed it and immediately jogged off to the sideline.
"I didn't even know he was out until I noticed him on the sideline and he didn't have his helmet on," right tackle Demar Dotson said.
Martin had an MRI on Tuesday.
Charles Sims and newly signed Jacquizz Rodgers were pressed into duty after Martin's injury, and the Bucs mustered only 85 rushing yards against the Cardinals. Jameis Winston had a career-high 52 passing attempts and four interceptions in the 40-7 blowout loss.
"Doug Martin means a lot to this team," Jameis Winston said. "Come on now. Doug is one of our best players. We love him tremendously. He had a great season. We just love having him on the team."
Martin was second in the NFL with 1,402 rushing yards in 2015, and he averaged 4.9 yards per carry. He averaged 18 touches in 16 games, accounting for nearly 72 percent of the Bucs' rushing yards from running backs last year.
"He's a tremendous running back," Dotson said of Martin. "He helps the offensive line out because we don't have to hold blocks for long. A guy like Chuck (Sims), he's a good running back. He's a guy [who] can hold the fort down."
Tampa Bay plays the Los Angeles Rams at home on Sunday.