Uganda's Moses Kipsiro added the 10,000m title to the 5000m crown won last week, beating Kenyans Daniel Salel and Joseph Birech in 27 minutes 57.39 seconds.
Matthews became the first New Zealand athlete to win two golds at a top competition, winning the three miles and the six miles at the Sydney Empire Games in 1938.
He also competed at the 1936 Olympics but had tendon problems after having to train on deck while sailing to Europe.
Matthews did not make the 5000m final in Berlin and was scratched from the 10,000m event.
