We demonstrate ultrafast resonant energy absorption of rare-gas doped He nanodroplets from intense few-cycle (∼10fs) laser pulses. We find that less than 10 dopant atoms "ignite" the droplet to generate a nonspherical electronic nanoplasma resulting ultimately in complete ionization and disintegration of all atoms, although the pristine He droplet is transparent for the laser intensities applied. Our calculations at those intensities reveal that the minimal pulse length required for ignition is about 9 fs. © 2011 American Physical Society.