"The medical tests revealed that Asamoah has ruptured the meniscus cartilage, while Rugani has strained the lateral collateral ligament, both in the right knee," Juventus said in a statement.
"The former is expected to undergo surgery with both players anticipated to return within around 45 days."
The news is a big blow to Juventus as defender Medhi Benatia is already out due to an injury, as is midfielder Claudio Marchisio. Young midfielder Stefano Sturaro has returned but is yet to play a game.
Those involved in win over Palermo, meanwhile, underwent a routine warm-down session in the gym while the remainder of the squad took to the Vinovo pitches for a mixture of fitness and ball work.
Juventus will visit Zagreb to play Dinamo Zagreb in a Champions League group stage match on Tuesday.
