Howard sustained ankle and foot injuries when he was tackled from behind in the second half of Sunday's 38-35 loss to the New York Giants.
Cameron Brate will see an uptick in snaps in the absence of Howard, who has recorded 34 receptions for 565 yards and a team high-tying five touchdowns. The 24-year-old's receiving yards rank fifth among tight ends while his touchdown total is tied for the third-most in the league.
Howard has collected 60 catches for 997 yards and 11 touchdowns in 24 career contests since being selected by Tampa Bay with the 19th overall pick of the 2017 NFL Draft.
Brate, 27, has 17 catches for 159 yards and three touchdowns this season for the Buccaneers (3-7), who host the San Francisco 49ers (2-8) on Sunday (1 p.m. ET).
Tampa Bay signed defensive back Josh Shaw to the available roster spot and added defensive end Demone Harris to the practice squad.
Shaw spent time with the Kansas City Chiefs earlier this season after playing three seasons with the Cincinnati Bengals. He has totaled 99 tackles and one interception in 51 career games since entering the league as a fourth-round pick of the Bengals in the 2015 NFL Draft.