The body of the 52-year-old from Hamilton was found about 7pm by a group who had taken their boat to the river near Ngāruawāhia, Detective Senior Sergeant Ross Patterson said.
Patterson said police are appealing for sightings of Isaac or any unusual activity around the area on the day.
Police had launched a homicide investigation following a post-mortem examination.
“To protect the investigation at this early stage, police are not in a position to elaborate further on the cause of death,” Patterson said.
“Police are continuing to piece together Mr Isaac’s movements in the days and hours leading up to his death and are appealing to anyone who may have seen or interacted with Mr Isaac in the days prior to Thursday January 18.”
Patterson said Isaac wasbelieved to have been travelling around the Hamilton area where he resides and was last seen wearing black cargo pants and a green camouflage pattern T-shirt.
“The investigation team would also like to hear from anyone who saw any unusual activity near the Waikato River at any of the bridges between Hamilton and Ngāruawāhia on the afternoon.
“Anyone who was out on the river or its pathways and banks and may have been recording recreational activities or taken photos or video on their phones is asked to please contact the inquiry team.”
People with information can call 105 or make a report online at 105.police.govt.nz by clicking “Update Report” and reference the file number 240119/8775.
Information can also be provided anonymously to CrimeStoppers by calling 0800 555 111.
“This is an incredibly distressing time for Mr Isaac’s whānau who are being supported by NZ Police and Victim Support,” Patterson said.
“The public can also expect to see an increased police presence along the Waikato River area while inquiries are conducted in the next few days.”