Savichev (Russian: Са́вичев) is a Russian surname. Notable people with the surname include:
- Daniil Savichev (born 1994), Russian footballer
- Nikolai Savichev (born 1965), Soviet and Russian footballer and coach
- Yulia Savicheva (born 1987) Russian singer
- Yuri Savichev (born 1965), Soviet and Russian footballer and coach
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