He tried to pull her back on to the platform but, running out of time, moved her to the side of the tracks instead, not knowing how fast the train was going or when it would stop.
Fortunately, the train was able to stop about 20m short of the spot where the woman fell.
Brown, who is trained in first aid, was then joined by other rescuers who helped get the woman on to the platform.
Nothing much went through his mind at the time except the thought that he needed to remove her from danger.
"I've got a lot of people calling me a hero but to be quite honest I wouldn't call myself a hero," he said.
"The train had stopped way before it came to where she was."
But Brown admitted he hadn't known at the time whether the train would have been able to stop or not.
He has stayed in touch with the woman as well and has received messages from grateful members of her family.
When the woman first fell on to the tracks, Brown had noticed her head "swaying", and said she "wasn't all there".
"I just thought 'oh my gosh', she's obviously either having a seizure or just fainted.
"Her head hit the ground so hard."
The woman regained consciousness soon after the incident, and was able to chat and laugh with Brown, apologising for making him late for work.
Metlink said in a statement it was great that customers on the platform moved the woman to safety, but they generally encouraged passengers to notify staff if there was somebody on the tracks.
"With 53,000 passenger journeys on Wellington trains each day, medical emergencies are a regular occurrence on the rail network. Our staff are trained in first aid and deal with these situations as best they can, but fellow passengers are often the first on the scene," Metlink said.
"It was great that the customers on the platform assisted in moving this customer to safety, although generally we ask customers to escalate any trespass situation to our staff and stay out of the rail corridor.
"For their safety we suggest that customers stand behind the yellow line on the platform to keep a safe distance from the edge."