Polite, somewhat old-fashioned term for a massage practitioner, often used with さん as a title. The base word is 按摩 (あんま).
See also: あん摩
I had the neighborhood masseur massage my shoulders.
From 按摩 (あんま, 'massage') + honorific さん. 按摩 is a Sino-Japanese word (按摩) originally referring to traditional Japanese massage.