The group arrived at Dark Lane Park, next to the bridge over Bage Way behind Shirehall, on Thursday and were served with an eviction notice requiring them to leave after complaints by nearby residents about antisocial behaviour.
One father who visited with his son was bitten by a dog and several people took to social media to report antisocial behaviour.
Christopher Geisler was in the park with his son when they were chased by the dog.
Mr Geisler, who went to hospital and was given an injection, said he was just relieved the animal did not attack his 11-year-old son Harry.
"All I cared about was getting my son off the site at the time," he added.
Another resident said one of the travellers was holding a chain and chased after a family who had come to use the park's play area.
Police officers were called and the travellers left on Thursday evening.
West Mercia Police said: "A Section 31 Notice has been served on those at that site and they have been instructed to vacate by 12pm on Friday."
Council workers were carrying out a tidy up operation on Friday following the group's departure.