"The driver failed to control the vehicle", Moscow Mayor Sergei Sobyanin said.
The taxi driver apparently tried to flee the scene, but was quickly apprehended by police. A medical source cited by Interfax said none of the people hospitalised was critically injured. He then flees the vehicle as bystanders attempt to apprehend him.
Asked if the driver appeared drunk, the witness said: "No, he wasn't drunk".
A view shows a damaged taxi, which ran into a crowd of people, in central Moscow, Russia June 16, 2018.
Police have detained the taxi driver who had a Kyrgyz driving license, the Moscow traffic authority wrote on social media.
Sources say the driver pleaded with people at the scene, claiming he did not mean to hit the football fans.
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Most African nations were upset about fellow nations from their continent voting for America's United bid . North America had 134 votes out of 200 possible ballots, with Morocco earning 65 from the panel.
Moscow Police have launched criminal investigation into a suspected violation of the traffic code.
Russian Federation is hosting the World Cup and the capital's streets have been crowded with foreign visitors.
The Mexican embassy in Moscow said two of its citizens were among the injured.
Russian authorities have pledged to stage a safe World Cup.