The former Liverpool midfielder challenged for a ball with Franck Kessie early in the first half but came out the worst for it, picking up a problem with his right ankle.
Can attempted to continue but could not make it past the half-hour mark, as he was forced to exit the contest in the 26th minute.
Replacing Can was a fellow German, Sami Khedira, who made his first appearance since February 15 against Frosinone.
Khedira had been sidelined with an irregular heart beat and was making his first appearance in the squad since returning, only to be summoned into action earlier than expected.
In his first year in Turin, Can has become one of the key men in Massimiliano Allegri’s midfield, appearing in 24 Serie A games and starting 15 of them.
He will now be evaluated following the match, with his status for the midweek clash against Ajax a major doubt.
The 32-year-old Khedira’s return will be an important boost for Juventus as Allegri deals with multiple injury questions ahead of Wednesday’s Champions League quarter-final against the Eredivisie giants at the Johan Cruyff Arena.
Cristiano Ronaldo headlines the question marks, as the star forward recovers from a hamstring injury sustained while on international duty with Portugal.
Winger Douglas Costa is also a doubt, as the Brazilian recovers from calf and thigh injuries. It was reported Costa would be fit to face Milan, but he did not make Allegri’s matchday squad.
Allegri has sounded out positive signals regarding both Ronaldo and Costa ahead of the first leg, as Juventus look to avoid a similar fate to the Portugal star’s former club, Real Madrid, who were shocked by Ajax in the round of 16.
In addition, Allegri has been without Martin Caceres, Mattia Perin, Andrea Barzagli and Juan Cuadrado.