They did not disclose what time the inmate escaped - or how.
They refused to release the name of the inmate but a source confirmed it was Strickland who is being treated for cancer.
Corrections is working with police to locate the Strickland.
"A full investigation will be held into the incident," the statement on Twitter said.
An ADHB spokeswoman confirmed the inmate "went missing earlier today".
"Auckland City Hospital activated security procedures designed to protect the safety of staff, patients and visitors, including limiting access to the hospital, and an increased security presence," she said.
"The hospital is open for patients and visitors.
"We are liaising with the police and the Department of Corrections."
She said contrary to some media reports the hospital was not locked down or closed off to other patients or visitors.
Police referred all inquiries about the alleged escape to Corrections.
