"The soil has already begun to crumble," warned the leader of the Diggers group, Vadim Mikhailov, speaking to the Life.ru news website.
The Diggers are a private organization whose members explore the tunnels and underground world beneath Moscow.
"Just imagine, there are tens of massive historical buildings. They can't all stand on nothing. Emergency measures need to be taken," he said.
Red Square sees parades and thousands of tourists every day, but Mikhailov warned that, "We shouldn't even walk on it, let alone hold parades!"
He said high-rise construction was partly to blame for many of the worsening problems underneath Moscow.
The newsmsk.com site pointed out that this was not the first time the Diggers had warned of apocalyptic scenarios for the center of the Russian capital.
A number of areas around the capital have seen small-scale collapses in recent years, and Mikhailov said that these would continue until the Moscow administration ceased "ignoring" the problem.
Specialists have warned that underground parking is creating problems for Moscow's foundations, and that some old and historical buildings are in genuine danger of total collapse.