Fire crews were called to the building at the corner of Cook and Nelson Sts about 5.30am.
Firefighters rescued two people who were asleep in an apartment where the e-scooter had caught fire, assistant fire commander Barry Thomas said.
Up to 300 residents were evacuated, he said.
Fire and Emergency New Zealand said the fire was in an apartment on the ninth floor.
Investigators would look into whether the e-scooter was charging or had been damaged in some way, Thomas told Morning Report.
Though there was a lot of smoke, the fire itself didn't go beyond the apartment, and was mostly extinguished by the sprinkler system, he said. The bedroom containing the e-scooter had the most damage.
Thomas said one of the people rescued was assessed by St John staff, and the other declined treatment.
"We don't like having to evacuate people from a large block at that time of the morning but it really was necessary at this time," Thomas said.
Evacuated residents have been allowed to return to their homes.
