It is understood a number of Mexican national's are among the injured.
"The preliminary cause of the accident is that the driver lost control of the vehicle", the Moscow police department said in a statement.
Another witness at the scene said of the taxi driver: "He was pulled out of the vehicle, he ran off but bystanders apprehended him".
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An unidentified official said of the injured: "Seven of them are in a satisfactory condition and one woman is in a moderate condition".
The witness added some of those hit were wearing Mexican team colours.
Russia is now hosting the World Cup and Moscow is one of 11 Russian cities where tournament games are being played. He was shouting: "'It wasn't me'".
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The agency that monitors Moscow's traffic safety said the driver is a citizen of the former Soviet republic of Kyrgyzstan who told police that the crash was not intentional.
Pictures released by the Moscow Traffic Authority show the taxi came to a stop next to a knocked-down traffic sign.
Russian authorities have vowed to host a safe soccer World Cup, which is taking place in 11 cities until July 15.
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