Police said the group, all in their late teens, had just left a nearby party and tried to get into the synagogue in Stamford Hill, north London, at about 01:15 on Sunday.
One man was punched in the face as he tried to stop them.
The six have been released on bail pending further inquiries.
Four men and two women were held on suspicion of public order offences and assault. Police said one man had made an anti-Semitic comment.
A Metropolitan Police spokesman said a number of people entered the synagogue on Craven Park Road, but they were removed shortly afterwards by security staff.
He added: "There is no suggestion that this was a far-right or extremist attack but rather the completely unacceptable actions of a drunken group."
But the incident is being treated as an anti-Semitic incident because of remarks made by one of the group.
The man who was punched was treated at the scene but did not require hospital treatment.
Six people arrested after a group forced its way into a synagogue in what police have described as an "anti-Semitic" incident have been bailed.