Employees, members and volunteers were advised of the plans on Friday.
The July winter Art Deco Festival will also not go ahead "for obvious reasons", chairman Michael Fowler said.
"It's such an important mid-winter event in the Hawke's Bay calendar. But with level 2 restrictions in place for a while, sadly we have no choice."
Fowler said the impact of the pandemic on the tourism elements of the trust's activities has been swift and dramatic.
"With New Zealand's borders closed to international visitors and domestic travel curtailed for the foreseeable future, our retail and tour operations have been hit hard and the board has agreed a restructure is the only option to ensure we remain viable.
"Cruise ships bring 100,000 visitors to Hawke's Bay every summer, a huge number of whom experience our walking tours, the retail store and our vintage car tours while they're in town," he said.
"These people, along with independent international tourists to Napier and people visiting family and friends in the Bay underpin the trust's profitability.
"With a drop in this trade, the retail store is simply not financially sustainable and there will be significantly lower demand for our walking and vintage car tours.
"The board agrees that if we are to ensure the future of the Art Deco Festivals and our heritage preservation activities, change is needed. That means proposing closing the retail store and scaling back our tours until the tourists return.
"Hawke's Bay's Art Deco heritage is unique in the world. It is our sincere hope that in the not-too-distant future international visitors will come back to experience it."
As 97 per cent of the 40,000 annual festival-goers are New Zealanders, the trust hopes to see a surge in interest for the 2021 summer festival.
"This will bring much-needed revenue to the trust, local tourism and accommodation operators and to Hawke's Bay."
The final number of employees impacted will not be confirmed for at least a week, until consultation has concluded.
