CCTV footage posted on social media showed the car veer out of a queue of stationary traffic and accelerate into pedestrians before coming to a halt said a BBC report.
The driver then fled pursued by several passers-by.
Moscow police said the driver was a 28-year-old national from Kyrgyzstan who was now being questioned in custody.
The city s mayor said the driver lost control of the car while Russia s Interfax news agency quoted an unnamed source as saying he had fallen asleep at the wheel.
An unidentified official said of the injured: "Seven of them are in a satisfactory condition and one woman is in a moderate condition."
The incident happened not far from the Kremlin and Red Square an area packed with tourists.
Russia is currently hosting the World Cup and promised "unprecedented" security measures in all cities hosting the games.
--IANS nir
