The 20-year-old, who joined from Bayer Leverkusen, was replaced by Jordon Ibe before making a prompt exit down to the tunnel to receive further treatment.
No obvious challenge caused the injury and Can was clearly in some discomfort before heading off the pitch but Rodgers has allayed concerns over the summer signing, claiming he was withdrawn simply as a precautionary measure.
"Young Emre was excellent; he showed some lovely touches on the ball," the Northern Irishman told Liverpool's official website.
"He's got power and pace. He just had a little bit of tightness in his calf, so as a precaution we took him off early on."
Rodgers' revelation means Can is likely to be available when Liverpool kick off their campaign against Southampton at Anfield on August 17, a match in which the club's other summer signings could make their bow.
Along with Can, Rodgers has brought in Rickie Lambert, Adam Lallana and Lazar Markovic following the departure of Luis Suarez and is set to announce the signing of Loic Remy, who has agreed to join the club from QPR.
Fabio Borini also started the match against Preston despite Rodgers confirming that Sunderland have agreed a fee to sign the Italian forward, who spent last season on loan at the Stadium of Light.