There are no managed isolation or quarantine (MIQ) facilities, or known Covid-19 cases self-isolating in either area.
Further samples will be taken in coming days, with results expected early next week.
The Ministry said anyone in the Hawke's Bay and East Cape with Covid-19 symptoms - no matter how mild - should get tested, even if they are vaccinated.
Gisborne Mayor Rehette Stoltz told RNZ's Checkpoint programme tonight the tests were from Monday and Wednesday.
She said the results could be from people who have recently returned from MIQ and urged everyone in the region with flu-like symptoms to get tested immediately.
"And also, get vaccinated."
The Ministry said vaccination rates in the Hawke's Bay have remained steady with 85 percent of residents having received their first dose, and 72 percent fully vaccinated.
In Gisborne, 79 percent of residents have received their first dose, and 65 percent are fully vaccinated.
"The Covid-19 vaccination is number one protections against the virus."
