A taxi drove into a crowd of pedestrians near Moscow's Red Square on Saturday, injuring eight people including two Mexicans in the city for the football World Cup which Russia is hosting, officials and eyewitnesses said.

The incident took place as residents and visiting football fans from around the world thronged the center of Moscow on a balmy summer evening.

Moscow's traffic management authority said the taxi driver had a driver's license issued in Kyrgyzstan, a mainly Muslim ex-Soviet republic.

The authority cited the driver, who was in police custody, as saying he had not driven into the crowd on purpose.

Moscow Mayor Sergei Sobyanin said in a post on Twitter: "There was an unpleasant incident with a taxi. The driver lost control of the vehicle."

The city's police said they had opened a criminal investigation into suspected violation of the traffic code.

Moscow city's healthcare department issued a statement saying eight people were hurt and had been taken to hospital. It said seven were in a satisfactory condition, while one woman was seriously hurt.

The Mexican embassy in Moscow said two Mexican women had been lightly injured. Also among those hurt were a Ukrainian and two Russian citizens, Russia's TASS news agency quoted a source in the emergency services as saying.

Video of the incident posted on social media showed the yellow Hyundai taxi pull sharply out of a line of stationery traffic, accelerate and mount the narrow pavement, which was packed with pedestrians.

The vehicle drove for about 10 meters along the pavement, bowling over pedestrians, with some of them being carried along on the bonnet of the car.

The taxi came to a partial halt after hitting a traffic sign. As bystanders tried to pull open the driver's side door, the driver, dressed in black trousers and black T-shirt, jumped out and sprinted away.

More bystanders chased after him and could be seen trying to tackle him to the ground as the footage ended.