Doss was hurt in the Colts' 27-24 season-opening loss at New England Thursday night, suffering a strained right hamstring while covering a New England punt return.
Doss, a second-year pro, was picked by the Colts in the 2003 draft out of Ohio State, and has become one of their most reliable defensive backs.
"He's done it," Dungy said Saturday. "He knows our defense. He's such a natural guy that he's able to play back there without a lot of practice."
Strickland played the last half of last season at safety.
The Colts, defending AFC South champions, next meet division rival Tennessee Sept. 19 at Nashville.