Klebanov graduated in 1974 from the M.I. Kalinin Polytechnical Institute in Leningrad where he majored in electrical engineering. After graduating, he moved up through the ranks of the Leningrad Optics and Mechanics Association (LOMO) in St. Petersburg, leaving in 1997 after spending 7 years as its Director.
From 1997-1998, he worked in the Saint Petersburg City Administration as a First Deputy Governor with responsibility for the economy and industrial policy. Klebanov was appointed the Deputy Prime Minister of the Russian Federation responsible for Military Industries in May 1998. He was instructed to reform the arms industry while in this post.
However, this endeavour was met with strong opposition, when he tried to cut the industry's 170 organisations down. He held that post until February 2002, when Klebanov was appointed Minister of Industry, Science and Technology. This move was seen as a demotion by many. On 1 November 2003 he was chosen to be the Presidential Envoy to the Northwestern Federal District.
It has been suggested that this was part of a long running campaign to bring the Northern capital closer to Moscow.