The Argentine striker was substituted after just 15 minutes following a collision with Torino goalkeeper Salvatore Sirigu early in the encounter.
Bernardeschi replaced Higuain but was himself taken off in injury time as the Bianconeri recorded a 1-0 win at the home of their city rivals.
"Higuain received a bruise and we'll evaluate him," Allegri told ESPN following the derby victory. "Bernardeschi left in the final stretch but there shouldn't be any problems.
"Starting Wednesday, we'll regroup with everyone available, but in any event, the team is feeling well and they showed it today."
Juve subsequently released a statement which read: "During today's derby against Torino, Gonzalo Higuain sustained a sprain and bruising of his left ankle, while Federico Bernardeschi sustained a knock to his left knee. For both players, further tests are planned in the coming days."