Officers are turning away runners and people walking their dogs.
The area around the Wintergarden Pavilion, including the cafe's outside dining area, has been cordoned off by police, and is guarded by a police car.
The main road through the Domain, from the Grafton entrance at Auckland Hospital is also cordoned off, however access to the pitches an the museum is open.
Early morning walkers and runners are still using the park, despite the rain and crime scene nearby.
Road closures will remain in place until at least 10am, police said.