By about 5.30pm, firefighters were damping down hotspots.
Grylls said the cause of the fire was undetermined and there would be an investigation into the cause.
Police also attended the incident and said it did not appear the fire was being treated as suspicious at this point.
A reporter at the scene was told by several people gathered nearby that the smoke had caught their attention from a distance.
Koinonia Kiripatea-Smith, who called emergency services, told the Post that the heat from the flames was "strong and scary".
She was driving back from Sulphur Point with her mother when she thought she saw fog coming from the direction of the museum.
"We carried on to the Government Gardens and we started to see smoke. By the time we got there the flames were 10-feet high and it was hot and the smoke was thick.
"Within two to three minutes it had spread up a tree which is how it got so high."
Kiripatea-Smith said people were trying to move their cars out of nearby parking spots as the fire took hold.
"I was standing about 150 feet from the flames and it is hard to describe that heat. It was strong and scary."
Rotorua Lakes Council, in a post on social media, said the fire was in the bush area alongside Queens Drive, near the Prince's Gate arches.
Councillor Tania Tapsell said the Government Gardens was a very important area for the community, "and I am pleased to hear the fire service responded as quickly as possible and did an excellent job at getting it under control quickly".