The rioters, protesting against the cartoons of the prophet Muhammad which appeared in Denmark's Jyllands-Posten, tried to storm the Norwegian-led peacekeeping base in the town.
According to the Norwegian military, 53 soldiers are in the base in the north west of Afghanistan on duty with the Nato-led International Security Assistance Force. 33 of those are Norwegian and five or six are Swedes. The rest are from Finland and Latvia.
"We have a Swedish observation group there which is based in the Norwegian camp," said Jan Jonsson from the Swedish military to TT.
"They were at the camp during the incident. But we have not had any information about injured Swedes," he said.
The rioting in the town, which has a population of 70,000, began at 6.30am Swedish time. The crowd managed to break through a gate and enter the compound, where they set fire to a vehicle. They occupied a building from which they shot at the soldiers.
The ISAF troops were forced to fire rubber bullets and tear gas as the demonstrators tried to attack the base. Two Dutch F16 aircraft also fired warning shots to disperse the crowd. Nato officials said that no shots were fired directly at the crowd.
One demonstrator was killed and several others have been taken to hospital. At least five Norwegians in the compound have been injured.
"The situation is very serious," a Norwegian officer, Thom Knustad, told Norway's Dagbladet.
On Tuesday afternoon the BBC reported that British troops are being rushed to the town to secure the airfield. A German military ambulance plane is on standby in Uzbekistan to fly to Meymaneh to pick up the wounded.