Spokesman Karl Angell said Saturday the man will be questioned but has not been charged. Two other men who were briefly detained in the crime have been released.
John A. Terry was found beaten and strangled at his home in early September. Police found his nude body and said his throat was tied with a cord and clothing.
The 65-year-old New Zealand native had lived in Jamaica since 1967 and was honorary consul for 13 years. He received a Member of the Order of the British Empire award in 1992 from Queen Elizabeth II.