The rest of the region is also expected to be quite windy.
A MetService spokeswoman said the warning was in place to give people a heads up about potentially hazardous driving conditions, debris which may blow around and time to tie down any outdoor items.
Temperatures will be cooler as the cyclone passes through, dropping to 18C in Napier and Hastings on Tuesday and Wednesday.
Rain is expected throughout the region on Tuesday, Wednesday and Friday with showers forecast on Tuesday particularly in the northern parts of Hawke's Bay but other parts of the region may be affected as well, the spokeswoman said.
High lying areas of the region can expect the most rain with 15-20mm in the ranges being an "optimistic" estimate.
Other parts of the region can expect up to 10mm of rain on Tuesday.
Less than 5mm of rain is expected on Wednesday and a period of rain late in the day on Friday will also be less than 10mm.
The region is extremely dry with a soil moisture deficit of between 30 and 50mm.
Federated Farmers Hawke's Bay provincial president Jim Galloway said last week the Government declared the whole of North Island in drought.
The farming industry in Hawke's Bay has incurred millions of dollars' worth of losses due to drought-stricken conditions facing farms in the region.
It meant farmers could receive Rural Support Trust funding, he said.
"The funding allows them to work with individuals and allows them to do feed co-ordination as well."
He said farmers across the region were already taking serious measures to prevent more losses.
"Farmers are sending stock out to someone else but that is a limited option, with everyone running out of water," Galloway said.
"In the higher country winter comes up quicker and some farmers might have to sell breeding stock. That's an extreme measure."
He said some dairy farmers who would be calving in autumn were calving now.
"The beans and sweet corn yields are well down as well," he said.
"All of this underpins the need for water storage, and if this carries on into the first couple of weeks of April it will impact a whole lot more farmers."
He said the key to getting through the 'big dry' was to look out for and after each other.