A deep clean of the fire station and a fire appliance was also being undertaken, Cooper said.
There was no information the contact had been identified as a positive Covid-19 case or even a close contact, he added.
"We're just being extremely cautious."
Crews from Napier and Bay View responded to the "minor" crash, alongside police, though only the Bay View crew came into close contact.
St John didn't respond to the crash.
Cooper said the risk of infection as a result of the PPE gear crews wear was "very minimal".
"I've spoken to the fire officer in charge this morning and will follow up later on."
Due to privacy reasons, he couldn't disclose the vaccination status of those involved.
A spokesperson for police confirmed they also attended the single-car crash where a car went into a bank on the side of the road.
"The sole occupant received minor injuries.
"A passerby who stopped to assist at the crash scene is an essential worker from Auckland who was carrying out permitted travel at the time."
The spokesperson said all Covid-19 protocols were followed by police staff and the people involved in the crash.
"Having considered all of the circumstances, no police staff were required to self-isolate."
Requests put to the Hawke's Bay District Health Board and Public Health Organisation were redirected to the Ministry of Health which has also been approached.