Increasingly detailed structural and dynamic studies are highlighting the precision with which biomolecules execute often complex tasks at the molecular scale. The efficiency and versatility of these processes have inspired many attempts to mimic or harness them. To date, biomolecules have been used to perform computational operations and actuation, to construct artificial transcriptional loops that behave like simple circuit elements and to direct the assembly of nanocrystals. Further development of these approaches requires new tools for the physical and chemical manipulation of biological systems. Biomolecular activity has been triggered optically through the use of chromophores, but direct electronic control over biomolecular 'machinery' in a specific and fully reversible manner has not yet been achieved. Here we demonstrate remote electronic control over the hybridization behaviour of DNA molecules, by inductive coupling of a radio-frequency magnetic field to a metal nanocrystal covalently linked to DNA. Inductive coupling to the nanocrystal increases the local temperature of the bound DNA, thereby inducing denaturation while leaving surrounding molecules relatively unaffected. Moreover, because dissolved biomolecules dissipate heat in less than 50 picoseconds (ref. 16), the switching is fully reversible. Inductive heating of macroscopic samples is widely used, but the present approach should allow extension of this concept to the control of hybridization and thus of a broad range of biological functions on the molecular scale.