Many of the infections are of the Omicron subvariants BA.4 and BA.5.
"Over the course of the past week, there has been a 57-per cent rise in new cases of COVID-19 compared to the previous week," Moscow social services wrote on Telegram, AFP reported.
"We recommend that you wear a mask in public places because the new Omicron subvariants BA.4 and BA.5 spread more rapidly from person to person."
For several weeks now, European countries have seen coronavirus infections rise again, largely due to the same Omicron subvariants.
The European Union on Monday recommended that all over-60s have a second vaccine injection because of the forecast "summer wave" in COVID infections. Its recommendation had previously been for people over 80.
Since July 6, the Russian capital has registered between 500 and 600 new cases daily, compared to less than 400 the week before.
This is still far from the high of more than 20,000 new cases per day recorded in Moscow in February this year.
Moscow has been the center of the pandemic in Russia. Waves that start in the capital quickly spread across the vast country.