Seven were in a satisfactory condition, according to a statement from Moscow city's healthcare department while one woman was seriously hurt.
The driver of the taxi, identified as 28-year-old Kyrgyz national Chingiz Anarbek Uulu, has been taken into custody.
WORLD Cup fans were among eight injured when a taxi crashed into pedestrians near Red Square in Moscow.
A video circulating on Russian social media and news websites showed the vehicle veering onto the pavement and hitting pedestrians.
Police said the driver in the crash was detained, and a criminal investigation had been opened. At the time, he didn't even have a full grasp of what he'd done, so his instinct kicked in and he tried to flee.
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The Moscow city government tweeted photographs of the yellow cab sustaining damage to its front bumper in the incident near the Kremlin and being towed away.
Moscow's traffic management authority said the driver was not drunk. Security throughout the country has been intense to make sure nothing untoward happens during Russia's home World Cup but having said that, bag searches at stadia, while thorough, have been for the most part been conducted respectively and courteously. When asked about this action, he said that he was afraid that the crowd will beat him.
Another witness, Viktoria Geraimovich, said she called emergency services on her mobile phone.
An eyewitness account from the police station published on a Russian Telegram channel showed the driver sitting handcuffed on a bench and looking dazed.
The Mexican Embassy in Moscow said on Twitter that two Mexican citizens were among the injured. "I was trembling. It is not a thing you see every day, when a taxi drives right into the crowd".
Russian Federation has instituted strict security measures nationwide as it hosts the World Cup soccer tournament, taking place in 11 cities over the next month.