Smoke swept through the airport's Terminal 2 building after the fire broke out in the departure hall, spurring authorities to seal off the area.
Operator Changi Airport Group said in a statement two people were sent to hospital for observation after approaching staff for medical assistance and four others were brought to a clinic at Terminal 3.
"A small fire occurred at the departure hall of Changi AirportTerminal 2. The fire has been extinguished by SCDF (Singapore Civil Defence Force)," Singapore police said in a statement.
Police said the fire alarm was activated at around 5:40pm (0940 GMT) as smoke poured from air vents.
Changi Airport Group said the affected terminal was shut to ensure passenger safety, and all departing and arriving flights moved to Terminal 3.
The SCDF gave the all-clear for Terminal 2 at 10 pm and airport authorities said operations there have resumed progressively.
"Changi Airport will do its very best and work through the night to clear the backlog of delayed flights," the operator said.
"A total of about 40 flights at Terminal 2 have been affected this evening. Changi Airport will work with authorities to investigate the incident."
An AFP reporter at the airport said the scene earlier was mostly calm as the departure and arrival halls were evacuated. Airport staff were also seen leaving but there was no panic.
M. Ramarao, an Indian software engineer working in Singapore, was set to take a flight back home with his 18-month-old daughter when they were evacuated.
"I am very worried now because we have a doctor's appointment tomorrow morning for my daughter who fractured her arm, so it's quite urgent," he told AFP.
"If it's for one or two hours it's okay, but they shouldn't cancel the flight."
About 58.7 million passengers from around the world passed through Changi Airport last year, making it the world's sixth busiest for international traffic.
The airport serves more than 100 airlines flying to some 380 cities worldwide.
