At least seven people have been injured after the vehicle ran into a group of pedestrians in the capital, Russian news agency TASS reports.
The driver attempted to flee the scene but was apprehended by police, a witness said.
The witness added some of those hit were wearing Mexican team colours.
Russian news agency Interfax has quoted a source as saying the driver may have been drunk.
Moscow Police said the driver likely lost control of the vehicle rather than deliberately steering his car into pedestrians.
The Moscow Traffic Authority has said the driver claimed he did not hit the crowd on purpose.
Pictures released by the Moscow Traffic Authority show the taxi came to a stop next to a knocked-down traffic sign.
The driver of the taxi has been detained, officials said.
They added the driver had a licence from the Central Asian nation of Kyrgyzstan.
This is a breaking story. More to follow…