Perry, a summer signing from National League One club Coventry, played starring roles during Bristol's stirring September victories over Bath and Newcastle.
But a hamstring injury suffered during the home league defeat against Gloucester then sidelined him, and Bristol have not won since.
"Shaun will add extra physicality," said Hill, as Bristol look to inflict a third successive Premiership away defeat on their mid-table rivals.
"Jake (Rauluni) has done well, but Shaun is a little stronger at getting the ball away from the breakdown and in getting behind the defence."
While Perry returns though, Hill is without the services of Samoan back Brian Lima (hamstring) and flanker Craig Short (ankle), with Short unlikely to play again until December.
Saracens have also lost a key performer to injury, with full-back Dan Scarbrough sidelined after recapturing the form that won him an England cap in 2003.
With Scarbrough out, Frenchman Thomas Castaignede moves from centre to full-back, with Dan Harris partnering Kevin Sorrell in midfield and Ben Johnston taking over from wing Ben Russell.
Another loss could leave Saracens 10 points adrift of the Premiership's top-four pace - hardly form to worry French giants Biarritz, their opening European Cup opponents on October 23.
"Bristol have had a good start to the season, and they have been playing some very good football," acknowledged Saracens head coach Mike Ford. "We are expecting them to test us."