The festival to mark the 325th anniversary of the Russian Imperial Guards is scheduled to take place on September 11-14 in central Moscow.
Military bands from the U.K., Austria, Ireland, Scotland, and Canada have been invited to the event. The Scottish bagpipers were due to leave for Russia on September 8.
A spokesperson for the Foreign Office said on Friday however that the Royal Regiment of Fusiliers would not be able to attend the Kremlin Zorya festival due to the crisis in relations between Russia and the West over the recent war in Georgia.
The bagpipers have been one of the most popular acts at the festival in recent years.
South Ossetia was attacked by Georgian forces on August 8. The majority of residents of South Ossetia hold Russian citizenship, and Moscow subsequently launched a massive operation to expel Georgian troops from the region and reinforce its peacekeepers. The operation, concluded on August 12, was called "disproportionate" by many Western leaders.
On August 26, Russia recognized South Ossetia and Abkhazia as independent states. Both republic broke away from Georgia in the early 1990s.