The Anger Management star apparently handed over the collector's item, autographed by the late baseball legend, to the 25-year-old actor during a house party, reported the Daily Mirror.
A source told the paper: "Charlie is a massive baseball fan. He is really proud of the array of stuff, old and new, that he has amassed and keeps it in a special room in his Los Angeles mansion.
"One evening he and Zac had been having a wild boys' night at Charlie's. Charlie showed him his collection and Zac was blown away by the 1920s signed Babe Ruth baseball. Charlie got it out and suddenly told him it was all his, that Zac could keep it."
They added: "Now he doesn't quite know how to ask Zac for the ball back."
Charlie is a big baseball fan and has starred in three baseball films: 1988's Eight Men Out, Major League in 1989 and its 1994 sequel.