Savichev (masculine, ) or Savicheva (feminine, ) is a Russian surname. Notable people with the surname include:
Daniil Savichev (born 1994), Russian soccer player, son of Nikolai Nikolai Savichev (born 1965), Soviet–Russian soccer coach and former player, twin brother of Yuri and father of Daniil Yulia Savicheva (born 1987) Russian singer Yuri Savichev (born 1965), Soviet–Russian soccer coach and former player, twin brother of Nikolai