They said the body was believed to be that of a missing person but were awaiting formal identification.
The scene has been cordoned off and a police guard remained there overnight.
Waitematā police issued a statement last week saying they had serious concerns for Wicksteed who had been missing for three months.
His family last heard from him in January and had recently reported him as missing.
Wicksteed was "typically known to frequent the Henderson area", a police statement said.
Local resident Arpit Joshi said it was "quite a shock" when several police cars pulled up at the end of their street on Friday afternoon.
"It was really sad to find out they found a body, and initially we were a bit scared, but police told us there was no danger."