Graham limped off the field with a right ankle sprain after his only carry during last week's victory over Minnesota and was placed on injured reserve Wednesday. That means a greater role in the offense for the 33-year-old Dunn.
"I expect to play a lot more. But at the same time, we have other guys who can come in and make plays," Dunn said. "I'm just going to do my part to help us move the chains, score touchdowns and win games."
Graham entered last season as the third-string tailback, but wound up playing a major role in Tampa Bay winning the NFC South because of injuries to Carnell "Cadillac" Williams and Michael Pittman.
He started 10 games and rushed for 898 yards and 10 touchdowns after gaining 215 yards and not scoring any TDs in his first three pro seasons.
Despite sacrificing some opportunities to carry the ball this season because the Bucs needed him to fill in at fullback, Graham is the club's leading rusher with 563 yards and a team-best four TDs.
"It's a big loss for us. ... Someone else will have to step up," coach Jon Gruden said.
Dunn, a five-time 1,000-yard rusher who was with the Bucs from 1997-2002 before spending the last six seasons with the Atlanta Falcons, has rushed for 476 yards on 109 carries and caught 26 passes for 207 yards this season.
"Warrick's got the ability to play in every situation. He relishes this time ... big games. He knows the team needs him to step up. But you have to do that, obviously, with some other players, too."
Graham's injury also could mean more playing time for Williams, who hasn't played in a game since September 2007 because of a serious knee injury.
The one-time NFL Offensive Rookie of the Year was moved from the physically unable to perform list to the 53-man roster last week, but was not active against the Vikings. There's a chance he may be held out this week against the Detroit Lions, too.
"We're trying to temper our enthusiasm and do exactly what we think is the right thing. That involves a lot of people's opinions. ... I'm kind of going with the flow," Gruden said, adding that concerns on special teams could play into the decision.
"I don't know that he'll play a major role in this game yet or not, or even if he will be active. ... It's not just about Cadillac. It's about our team. ... That fourth, fifth receiver, the extra backs on everybody's team have got to play on [special] teams because we all know that special teams are going to be a key component here down the stretch."
Fourth-year pro Noah Herron was signed to fill Graham's spot on the roster. He has appeared in 23 games with Green Bay and Pittsburgh, rushing for 273 yards and three touchdowns and catching 29 passes for 211 yards and two TDs.
The Bucs also placed rookie linebacker Geno Hayes (knee) on injured reserve and signed linebacker Matt McCoy, who played in three games for Tampa Bay before being released on Oct. 18. Hayes was injured covering a kickoff against the Vikings.