The convoy drove on to Selly Oak Park, on Gibbins Road, which is close to Birmingham University and other attractions, on Tuesday evening.
The sudden encampment prompted an early-morning visit from police.
Coun Karen McCarthy (Lab) said she was waiting for an update from the council.
She said: “It’s really disappointing that it has been targeted in this way.
“It’s used by a lot of the residents, there’s a children’s play area, an outdoor gym, so everybody from families to students.
“The Scouts are based in the Scout hut, so there will be disruption.
“It’s not a park that can be easily secured because even though there’s a gate, there isn’t a fence along Gibbins Road.
“We are hoping the council and the police will be able to take action.”