Pelyevina, who is coordinator for the organization Committee for Democratic Russia, told Interfax that City Hall based the refusal on the grounds that the event "may influence the judicial process" in the Magnitsky case.
The group had planned an event for March 24 on Kaluzhskaya Ploshchad as a show of support for Magnitsky's relatives and to protest what it called "police violence" in the case.
Magnitsky was arrested on tax evasion charges after he began investigating the roles of Interior Ministry and tax service officials in an alleged fraud case. He died in detention in 2009, having been denied treatment for a variety of ailments, in a case that has caused international outrage.
The case against Magnitsky was dropped after he died but has since been re-opened. Two prison officials have been charged in connection with his death.
"The organizers want to demand a fair investigation into the death of the lawyer who uncovered large-scale corruption in the security and tax services, and to bring those responsible to justice," Pelyevina said.
Pelyevina said her group will appeal the city's decision and will hold one-man pickets instead of a rally if the appeal fails.