The moves were made Tuesday, two days after Urbik hurt his right knee in a 38-14 loss at Minnesota. Urbik started the game at right guard, but was hurt filling in at center after Geoff Hangartner hurt his right knee.
Hangartner has been ruled out from playing Sunday, when Buffalo (2-10) hosts Cleveland (5-7).
Rinehart signed with Buffalo in October after being released by the Jets. He appeared in five games with Washington over the previous two seasons. The Bills also signed center Sean Allen to their practice squad. Allen rejoins Buffalo after being released last summer.