We demonstrate experimentally picosecond all-optical control of a single plasmonic nanoantenna embedded in indium tin oxide (ITO). We identify a picosecond response of the antenna-ITO hybrid system, which is distinctly different from transient bleaching observed for gold antennas on a nonconducting SiO(2) substrate. Our experimental results can be explained by the large free-carrier nonlinearity of ITO, which is enhanced by plasmon-induced hot-electron injection from the gold nanoantenna into the conductive oxide. The combination of tunable antenna-ITO hybrids with nanoscale plasmonic energy transfer mechanisms, as demonstrated here, opens a path for new ultrafast devices to produce nanoplasmonic switching and control.