Heinesen is a Faroese name. Notable people with the surname include:

Elin Brimheim Heinesen (born 1958), Faroese journalist Jens Pauli Heinesen (1932–2011), Faroese writer Knud Heinesen (1932–2025), Danish politician William Heinesen (1900–1991), Faroese writer Zacharias Heinesen (born 1936), Faroese painter