"The man was no longer there after being asked to leave by the occupants," a spokesperson said.
The spokesperson said the man was believed to have been intoxicated.
It was believed he had "mistakenly" gone to sleep in the wrong house.
Fairfax reported the baby's mother had posted on Facebook about the incident, asking for information about the intruder.
The couple gave him a towel and then kicked him out, she said.
The man was described as being Māori or Pasifika, clean shaven, with short hair.
He also had a tattoo on his neck.