Johnson, second on Carolina's all-time sacks list, suffered the injury in the second half of Sunday's 27-22 victory over New Orleans and did not return.
It is the same hamstring that kept Johnson out of most of training camp and hampered him at times last season.
But the Panthers (3-0) may get middle linebacker Luke Kuechly back after the two-time Pro Bowler missed the past two and a half games with a concussion.
Coach Ron Rivera said Kuechly is scheduled to meet with the independent physician Tuesday. He said Kuechly had a good checkup with team doctors Sunday and progressed another step in the concussion protocol.
"If it's good news [Tuesday], then we can get him rolling on Wednesday," Rivera said.
Rivera said Johnson will be re-evaluated after the bye week, which follows the Tampa Bay game. He was unaware if the hamstring was torn or tweaked.
"We'll see how long it'll be," Rivera said. "But he most certainly will be out this week for sure. ... Hopefully, [the bye] will give it time to calm down a lot and get some strength back, and we'll see how he is coming out of the bye."
Rivera said end Rakim Cox could be brought up from the practice squad. The Panthers also have tried out several other ends the past two weeks.
Rivera said outside linebacker Thomas Davis, the 2014 NFL Man of the Year, suffered a pectoral injury and will undergo an MRI. He was uncertain of Davis' availability for Tampa Bay.
Running back Jonathan Stewart took a shot to the calf late in Sunday's game, forcing the Panthers to turn to rookie Cameron Artis-Payne at a critical time. Rivera said there was no concern with having Stewart available for the Buccaneers.
Carolina is 3-0 for the first time 2003, the team that went to the Super Bowl.