She replaces Katie Grand, who founded the magazine in 2000 but quit in October to work on Conde Nast's rival launch Love.
Zhukova's appointment comes as Pop opens a new London office, a satellite office and installation space in Berlin and a partnership with The Saatchi Gallery in London.
Zhukova, the daughter of Russian oligarch Alexander Zhukov, has been involved in various business ventures in the fashion and design fields.
She is the founder of The Garage Center for Contemporary Culture in Moscow, which opened last September to promote international contemporary art and culture.
In her new role Zhukova will work in partnership with editorial director Ashley Heath, former fashion director of The Face, who conceived and co-launched Pop.
Zhukova and Heath have interviewed and appointed a new team who will work from the new office in London.
David Davies, managing director of Pop and Bauer Media's women's portfolio, said: "Dasha's formidable recent track record and reputation worldwide means we have a truly exceptional and talented editor-in-chief to replace Katie Grand and take Pop to a whole new level."
Zhukova said: "We are working hard on a complete revamp of the magazine in order to provide a broader point of view focusing also on art, contemporary culture and the globalisation of all things pop related."
Bauer Media has also appointed former executive Tom Bailey as associate publisher of Pop.
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