At the rally far-right leader Oleh Tyahnybok, who heads the Svoboda party, urged the authorities to return "Hero of Ukraine" status to Bandera.
Many Russians revile Bandera, born on 1 January 1909.
President Vladimir Putin has called him "Hitler's accomplice".
Russia says it supports separatists in eastern Ukraine because of a neo-Nazi threat to ethnic Russians.
WW II echoes
Marchers carried the nationalist flags of Svoboda and the Right Sector - both movements that helped to topple ex-President Viktor Yanukovych, who was an ally of Moscow, last February.
Some marchers also wore World War Two nationalist uniforms.
Turnout at the rally was estimated at 2,500.
Russia says some Russian TV journalists were assaulted at the Kiev march.
Two women reporters with the pro-Kremlin TV channel LifeNews were "attacked" by masked assailants, who smashed their camera and stole a mobile phone, the Russian foreign ministry said.
"This is the latest glaring instance of the media being persecuted in Ukraine for doing their job," ministry spokeswoman Maria Zakharova said.
A man has been arrested in connection with the incident, Ukraine's Unian news agency reports.
Bandera is a controversial figure in Ukraine.
His "hero" status was revoked by Yanukovych.
Despite leading anti-Soviet resistance fighters, Bandera was arrested and jailed by the Nazis during the war.
He was assassinated by a Soviet KGB agent in Munich in 1959.
Source: BBC News Europe