Abu-Assad was born to a Palestinian Muslim family, in the city of Nazareth, Israel in 1961. He immigrated to the Netherlands in 1981, where he studied aerodynamics in Haarlem and worked as an airplane engineer for several years. Abu-Assad was inspired after watching a film by Michel Khleifi to pursue a career in cinema. Abu-Assad initially started as a TV producer working on commissions for Channel 4 and the BBC. He founded Ayloul Film Productions in 1990 with the Palestinian film-maker Rashid Masharawi.

In 1992, Abu-Assad wrote and directed his first short film, Paper House which was made for NOS Dutch television and won several international awards at film festivals in Paris and Jerusalem.

In 1998, he directed his first film, Het 14de kippetje (The Fourteenth Chick), from a script by writer Arnon Grunberg. Later films include the documentary Nazareth 2000 (2000) and the feature film Rana’s Wedding (2002).

In 2006, his film Paradise Now won the Golden Globe Award for Best Foreign Language Film, and received an Oscar-nomination in the same category. In 2005 Paradise Now won the Golden Calf for Best Feature Film at the Netherlands Film Festival.

His 2013 film Omar was screened in the Un Certain Regard section at the 2013 Cannes Film Festival where it won the Jury Prize. In 2014, Omar was the Palestinian entry for the Best Foreign Language Film at the 86th Academy Awards, and was nominated for the award. The film also won the award for Best Film at the Asia Pacific Screen Awards.

In 2014, Abu-Assad was invited to join the Academy of Motion Picture Arts and Sciences.

In 2018, Abu-Assad joined the film jury for ShortCutz Amsterdam, an annual film festival promoting short films in Amsterdam.