Midfielder Can, who joined from Liverpool on a free transfer in 2018, has been overlooked in favour of Sami Khedira, Blaise Matuidi, Miralem Pjanic and new signings Aaron Ramsey and Adrien Rabiot.
Mandzukic, who scored in the Champions League final defeat to Real Madrid in 2017, misses out in favour of Gonzalo Higuain, Cristiano Ronaldo, Paulo Dybala, Juan Cuadrado and Federico Bernardeschi in attack.
Head coach Maurizio Sarri expressed concern last month that he would be forced to omit senior players from the 22-man list for the group stage given the size of his squad.
He branded the club's transfer policy "embarrassing" as Juve struggled to offload stars to accommodate the arrivals of several new players, including Rabiot, Ramsey, Matthijs de Ligt, Danilo, Luca Pellegrini, Merih Demiral and Gianluigi Buffon.
"We have to cut six players from the Champions League squad," he said. "If we don't, the choices we have are crazy.
"The last 20 days of the [transfer] market will be difficult for us. It's a difficult, embarrassing situation, because we risk leaving top players out of the squad list.
"It's a situation we have to resolve, and it's not strictly connected to the choices of the coach or club."
They begin their campaign against Atletico at the Wanda Metropolitano on September 18.