The victim was taken to hospital and received four stitches just above his eye, the publication reported.
It is understood Starr is in Spain filming for a new Guy Ritchie film.
In court, the actor was told that he would only escape having to serve prison time if he paid his young victim £4000 ($7855) within three days.
A court official told the newspaper: "The detainee's state of drunkenness was taken into account as an extenuating factor.
"The sentence was the result of an agreement between the state prosecution service and the man who was subsequently convicted."
The victim told local media that after Starr punched him, he felt dizzy and it was at that point the actor hit him with a glass.
It is also alleged that the New Zealand-born actor later yelled out to him: "You don't know who you've messed with. You don't know who I am and what you've done."
As well as his role on The Boys, Starr is widely known for his acting role as twins Van and Jethro West in local drama Outrageous Fortune.