Among the honours that Matsushima received, perhaps the most prestigious was the Asahi Prize which was presented to him for his research on continuous groups in 1962.
Sa hanay ng honours na Matsushima natanggap, marahil ang pinaka-prestihiyoso ay ang Asahi Prize na kung saan ay ipinapahayag sa kanya para sa kanyang mga pananaliksik sa patuloy na grupo sa 1962.