Zhukov was born in Nizhny Novgorod in 1936 but his family moved to Moscow in the following year.
He graduated in 1960, having won second prize in the Long-Thibaud Piano Competition in Paris.
Apart from a career as a pianist, Zhukov also conducted his own ensemble, the Moscow Chamber Orchestra until his retirement from conducting in 1994, and was the pianist of the long-running Zhukov Piano Trio which was founded in 1963 and continued performing until 1980.
The trio was noted for its "Historic Concerts" which featured repertoire spanning the 17th to the 20th centuries.
Zhukov made recordings on the Melodiya/CBS label, among others (e.g. the complete Scriabin sonatas).