The decision came with only three days left for the opening ceremony of the festival, which was to have gone on until June 26.
If the pandemic is controlled, the festival could take place in late July, the authorities said.
Held just after the Hue Festival, one of the country's biggest tourism events, the craft festival honors artisans and traditional craft villages and features a slew of cultural and entertainment activities.
The Hue Festival, scheduled to be held in August last year, was postponed to this year but no exact date for it has been released so far.
Hue, capital of Thua Thien-Hue Province and renowned for its Imperial Citadel and royal tombs, received over 4.8 million visitors in 2019, 2.1 million of them foreigners.
In the ongoing fourth wave of Covid since April 27, Thua Thien-Hue has reported five infections.