Genetically modified viruses have been proposed recently as templates for the assembly of nanometer-scale components of electronic circuits. Here we show that, in addition to their role as nanotemplates, viruses can actually improve the electron transport properties in semiconductor nanotubes grown on them. In the considered hybrid virus-inorganic nanostructures, which consist of silica or silicon nanotubes deposited on tobacco mosaic viruses, the confined acoustic phonons are found to be redistributed between the nanotube shell and the acoustically soft virus enclosure. As a result, the low-temperature electron mobility in the hybrid virus-silicon nanotube can increase by a factor of 4 compared to that of an empty silicon nanotube. Our estimates also indicate an enhancement of the low-temperature thermal conductivity in the virus-silicon nanotube, which can lead to improvements in heat removal from the hybrid nanostructure-based nanocircuits.