Zvyagintsev (Russian: Звягинцев) is a Russian surname. Notable people with the surname include:
- Andrey Zvyagintsev (born 1964), Russian film director
- Vadim Zvjaginsev (born 1976), Russian chess player
- Vasily Zvyagintsev (1944–2016), Russian author
- Viktor Zvyahintsev (1950–2022), Soviet retired footballer