Detective Senior Sergeant Paul Newman said the 72-year-old man was playing with his grandchildren when he was approached by a man aged his his late teens or early. 20s.
The young man tried to lure the man away and when he was ignored, he cut the elderly man with a knife.
There were about 20 people in the park at the time.
Newman did not want to say how old the man's grandchildren are, or how they are coping, but said the whole family is being supported.
The man himself was "doing alright", Newman said.
"His injuries are thankfully minor."
Newman said the young man had tried to engage the pensioner in conversation, but he would not give details on the nature of the conversation.
The man had tried to walk away before he was attacked.
"There's been no argument, no provocation."
The weapon was described as "similar to a knife" but he did not have further details.
"It's very concerning. We really want to appeal to people for information."
The public should be careful and alert police if they notice any suspicious activity.
Victim 'struck in the neck'
The man was the victim of an unprovoked attack, police say.
The 72-year-old suffered a deep cut to his neck at Little Rangitoto Reserve about 4.30pm.
A police spokeswoman said they are looking for witnesses.
The man was at the park with family members when a man approached him, said police.
"An altercation has taken place and the victim has been struck in the neck, receiving a deep cut."
Detective Senior Sergeant Newman said: "The victim and his family are obviously very shaken."
They were being supported by police, and a number of staff were working on the investigation.
"We want to assure the public that we are making a number of enquiries, including an area canvas and speaking with neighbours."
There would be an increased police presence in the area while the investigation continued, he said.
The offender is described as Caucasian with olive skin and of medium build. He was wearing dark clothing and was last seen running down Upland Rd, towards Benson Rd.
Anyone in the reserve, or surrounding areas on Upland Rd, yesterday between 4pm and 5pm, and who witnessed any suspicious behaviour, should call the Auckland City Crime Squad on (09) 302 6557 or, anonymously call Crimestoppers on 0800 555 111.