The protest, one of the biggest seen in the capital in years, was against the Russian government’s “digital sovereignty bill”.
The bill requires all internet traffic in Russia to be directed through state-controlled routing points, would reduce Russia’s dependence on the United States.
The government says the bill will improve cyber-security, but campaigners say it is an attempt to increase censorship and stifle dissent.
Activists say more than 15,000 people gathered in Moscow on Sunday, which is double the estimate given by the police.
Protesters chanted “hands off the internet” and “no to isolation, stop breaking the Russian Internet”.
“If we do nothing it will get worse,” one protester told Reuters news agency. “The authorities will keep following their own way and the point of no return will be passed.”
Another campaigner, Sergei Boiko, told AFP news agency that “the government is battling freedom”.
“I can tell you this as somebody who spent a month in jail for a tweet,” he added.
Opposition figures said that a number of protesters were detained in Moscow, but the police have not confirmed this.
A second vote is expected later this month. If it is passed it will eventually need to be signed by President Vladimir Putin.
View this news report from EuroNews below: