Police in the county of Surrey, outside of London, did not name the man.
Two children survived the shootings of their mother, father and grandmother in September 2012.
Saad al-Hilli, his wife, Ikbal al-Hilli, and his mother-in-law were shot dead, along with a French cyclist.
Zainab al-Hilli, 7 at the time, was shot and beaten but was rescued by a British cyclist who came upon the scene.
Her sister Zeena, 4 at the time, hid under her mother’s body in the family car and survived physically unharmed.