Klyuyev or Klyuev () is a Russian surname. Notable people with the surname include:
Aleksandr Klyuyev, Russian football player Andriy Klyuyev, Ukrainian businessman and politician Boris Klyuyev, Russian actor Denis Klyuyev, Russian football player Nikolai Klyuev, Russian poet Serhiy Klyuyev, Ukrainian businessman and politician Yury Klyuyev, Russian speed skater