Mr Dennis helped arrange for the youth to move to Australia. He subsequently returned to New Zealand, and his family complained about Mr Dennis's involvement.
Opposition parties have said the leak about the investigation is an example of dirty politics and a sacking offence - but Mrs Bennett says the staff member assumed the information was in the public arena.
"My staff member very much regrets this error and has apologised to me and I accept their assurances it won't happen again. I have made it clear that it was not appropriate," Mrs Bennett said in a statement.
"I have called Mr Dennis to offer my apologies in person."
On her way into Question Time, Mrs Bennett confirmed that Mr Dennis had told her of the police investigation during a private meeting on Friday.
"I have heard that there is an investigation currently, but I have no idea of any details or anything like that."
Asked by Radio New Zealand if her office had been making unsolicited calls to journalists to let them know about that cafe conversation or the police investigation, Ms Bennett said not that she was aware of.
In a follow-up statement issued this afternoon, Mrs Bennett said she a member of her team had told her they had discussed the police investigation with a reporter, "briefly at the conclusion of a phone call about a work matter".
"The staff member in question assumed the information was in the public arena."
TVNZ has confirmed that a One News reporter, based outside of the Parliamentary press gallery, was contacted by a staff member from Mrs Bennett's office.
On what disciplinary action the staff member involved could face, Mrs Bennett said it was an employment matter and confidential.
Mr Dennis has been contacted for comment, as has Te Puea Marae.
A police spokesman confirmed Mr Dennis was stood down from duties on September 21 last year pending a police investigation.
"Police have nothing further to comment on this investigation at this time."
Mr Dennis has been leading efforts by the marae to help 27 families and individuals to move to social housing, places in families' homes and motels.
The Manukau Urban Maori Authority has found jobs for several adults, and Whanau Ora services are being offered to all the families.
Ministry of Social Development staff have been working at the Mangere marae since it opened up to receive homeless families last month.
This morning Mrs Bennett made a short visit to the marae. She said she wanted to make sure homeless people were linked to other public services such as education, social work and counselling.
Labour's housing spokesman Phil Twyford said it was unthinkable that Mrs Bennett's staff member would go "rogue".
"Political staff would not take such serious unilateral action without the knowledge of their Minister. Their job is to act in the best interest of their boss."
Earlier today, NZ First leader Winston Peters said he did not know the details, but if the allegations were true it would be a sacking offence for anyone involved, including Mrs Bennett.
Maori Party co-leader Marama Fox said: "I couldn't even wonder why we wouldn't be more focussed on trying to get those families into homes rather than muddying the waters with tid bits of information."
Green Party co-leader James Shaw said the allegations were very serious, and needed to be cleared up.
