Faig is both a given name and a surname. Notable people with the name include:
Faig Aghayev (born 1971), Azerbaijani singer Faig Ahmed (born 1982), Azerbaijani artist Faig Azizov (born 1966), Azerbaijani footballer Faig Garayev (born 1959), Azerbaijani volleyball coach Faig Gasimov (1974-2020), Azerbaijani lieutenant colonel Faig Hajiyev (born 1999), Azerbaijani footballer Faig Jabbarov (born 1972), Azerbaijani footballer Faig Mammadov (1929–1987), Azerbaijani agronomist Mario Faig (1905–1984), Argentine film actor Miquel Faig, Spanish economist Omar Faig Nemanzadeh (1872-1937), Azerbaijani publicist