The cause of the fire is unclear but Port chief executive Mark Cairns said that fires in the forklifts were not uncommon, and that was why dry powder extinguishers were readily available.
Mr Cairns said although the forklift suffered extensive damage, no one was hurt and no other objects were damaged from the fire.
"It's nothing significant from what our security staff say.
"There was a machine fire, it was put out."
In March a large log-loader caught fire at the port, with an estimated damage bill of $1.5 million.
But Mr Cairns did not anticipate the cost from the forklift fire would be great.
"It's a small forklift," he said.