Emergency services were soon on the scene, searching the wider area with several boats in the outgoing tide, assisted by the Lowe Corporation Rescue Helicopter.
The deceased student lived with a New Zealand family but had close relatives living in Hawke's Bay, with more flying to New Zealand from Korea after hearing the bad news.
The family had hosted students for 15 years "and have been bringing most of them down here to swim in the summer and have never had a problem", the spokesman said.
The student's body was found close to where he entered the water.
Napier resident Wanita Rarere said there should be signs at the estuary warning people.
"They [tourists] ask me to take pictures of them and I try to warn them but they don't understand - I try to show them with sign language but they don't get it," she said.
Napier Mayor Bill Dalton said while there were signs on the beach near the Napier CBD, warning swimmers of the potential for difficulty, "you can't have signs everywhere".
"We could have a world with warning signs wherever there's water but at the end of the day a large part of this comes down to individual responsibility," he said.
"I feel very sad for the young man that has lost his life but we cannot go around putting signs everywhere there is the potential for danger, or we would live in a world that is completely covered in signs."
The director of New Horizon, Ewen Mackenzie-Bowie, was due to fly to Hawke's Bay from Auckland yesterday afternoon.
"Our team are liaising with the police and a lot of people are traumatised," he said.