All departing flights were canceled after the protesters broke into the passenger terminal, Serirat Prasutanond, the director of Suvarnabhumi airport, said. There are also demonstrators sitting on the road in front of the terminal, video of the protest showed.
They are trying to prevent Thai Prime Minister Somchai Wongsawat from returning to the country from an international summit in Peru.
Protesters carrying golf clubs and long wooden sticks clashed with airport taxi drivers, with each side throwing objects at the other. Lightly-armed police with plastic riot shields were at the scene attempting to restore order.
Airport officials said incoming flights would be allowed to land because there is not enough time to divert planes to other airports.
CNN's aviation expert, Richard Quest says Suvarnabhumi is one of the major hubs in Asia for travelers going on the "kangaroo route" connecting Australia with Europe.
He said Tuesday's incident will add to a litany woes that have beset the terminal since it opened two years ago. "The crucial thing to note is that Suvarnabhumi has had a very checkered past. It nearly collapsed when it opened and there were all sorts of other horrendous issues."
The anti-government People's Alliance for Democracy (PAD) has been protesting since May, accusing the government of being a front for ousted former Prime Minister Thaksin Shinawatra.
Pro- and anti-government protesters exchanged gunfire earlier in the day, a Thai police official said. Eight people were injured, said the police officer, who asked not to be named. No deaths were reported. The injuries were minor, and the wounded were sent to Sau Paulo General Hospital.