"I just entered the store 10 minutes before and we're in the second aisle when the sirens went off and we were asked to leave our trolleys and to evacuate.
"At first there was confusion and people wouldn't move and then staff became insistent."
Grobler said she did not see anything specific but could smell smoke.
"It was absolute chaos to get the people out and like a stampede to get back in.
"People were crowding around the door to get back in but staff ushered people to get across the road.
"It was only about 45 minutes or so that we were outside and then back in."
Customers at the neighbouring Westgate mall saw fire engines rushing to the newly opened Costco New Zealand store just before 4pm.
Fire and Emergency services attended the incident but said there were no reports of active flames.
"Two fire and a ladder truck are on scene. A fire alarm has been activated. We don't know much yet," FENZ said earlier.
A video showed a massive crowd of people gathered outside the store following the evacuation.
Traffic cones were laid outside the front of the store.
Some people were also filming the scene with their mobile phones.
Earlier this morning, a member of the public posted on social media suggesting there had been a brawl at Costco, that security told people to leave and trespassed them.