The man is deemed to be in police custody, Detective Inspector Scott Beard said. No formal charges had been laid "at this early stage".
Police described the double homicide as a "family harm-related incident".
Beard said autopsies would be performed today on the man and woman found fatally stabbed in their Epsom home.
A fourth person who received superficial injuries in the incident had now been discharged from hospital and was interviewed by detectives yesterday.
"Police would like to remind the local community that at this stage police are not seeking anyone else in connection to the incident, and we do not believe there is a wider risk to the public as this appears to be a family harm-related incident," Beard said today.
'Who would kill them?'
AUT lecturer Ranjana Gupta told the Herald yesterday she was shocked to learn her former neighbours were both dead.
"Who would kill them? I cannot understand that. There has to be some kind of motive behind the killing."
Emergency services rushed to the property at the intersection of The Drive and Green Lane West after being alerted about 11.30am.
They found two people with critical injuries who died despite paramedics' attempts to save them. A critically injured man was also discovered at the house and taken to Auckland City Hospital.
A fourth person – believed to be a passerby who tried to intervene – suffered superficial injuries and was able to speak to police.
Police confirmed yesterday they were investigating a double homicide and the individuals involved in the tragedy were known to each other.
"This was not a random attack," Beard said.
The woman – who worked at the University of Auckland - would sometimes visit Gupta's house to help with computer problems.
It's understood the woman's husband worked at Fisher & Paykel Healthcare.
The couple immigrated to New Zealand from the Indian state of Goa and moved into the block of flats about 2007 because it was in zone for Auckland Grammar where their son attended.
"She was a very good lady," Gupta said.
"They are Christian; they used to go to church. They were very God fearing. They were very humble sort of people. They were very helpful as well. They used to look after our property when we're not there."
She received a call yesterday from her son telling her of the deaths, Gupta said.
"To be honest it's shocking. I cannot see any reason why they would kill them. It's just beyond my thinking."
