Tessier and Teissier are surnames of French origin. Notable people with the surname include:
- Albert Tessier (1895–1976), French-Canadian priest, historian, and filmmaker
- Bernard Teissier (born 1945), French mathematician
- Charles Tessier (c. 1550 – after 1604), French composer and lutenist
- Christian Tessier (born 1978), Canadian actor
- Claude Tessier (1943–2010), Canadian politician from Quebec
- Dan Tessier (born 1979), Canadian professional ice hockey player
- Élizabeth Teissier (born 1938), French astrologer and former actress
- Emilie de Tessier (1850–1890), French cartoonist who worked under the pseudonym Marie Duval
- François-Xavier Tessier (1799–1835), Canadian doctor, publisher, and political figure
- Guy Teissier (born 1945), Member of the National Assembly of France.
- Henri Antoine Marie Teissier (1929–2020), French Catholic Bishop, Archbishop Emeritus of Algiers
- Joseph-Adolphe Tessier (1861–1928), Canadian politician from Quebec
- Jules Tessier (1852–1934), Canadian lawyer and politician from Quebec
- Mary Teissier (1917–1990), Ukrainian-French socialite and mistress of J. Paul Getty
- Odette Teissier du Cros (1906-1997), French ethnologist, curator
- Orval Tessier (1933–2022), Canadian professional ice hockey player
- Paul Tessier (1917–2008), French surgeon in the field of craniofacial surgery
- Pierre Le Tessier (1255–1325), French cardinal
- Robert Tessier (1934–1990), American actor and stuntman
- Thomas Tessier (born 1947), American author of horror novels and short stories
- Ulric-Joseph Tessier (1817–1892), Canadian lawyer, judge, and politician from Quebec