"examination of the breast by means of X-rays," by 1937, from mammo- "breast" + -graphy.
Entries linking to mammography
mammo-
word-forming element meaning "breast," from Latin mamma "breast" (which is cognate with mamma). The form mammato-, used in cloud terminology in reference to smooth, rounded shapes, is from Latin mammatus.
-graphy
word-forming element meaning "process of writing or recording" or "a writing, recording, or description" (in modern use especially in forming names of descriptive sciences), from French or German -graphie, from Greek -graphia "description of," used in abstract nouns from graphein "write, express by written characters," earlier "to draw, represent by lines drawn," originally "to scrape, scratch" (on clay tablets with a stylus), from PIE root *gerbh- "to scratch, carve" (see carve).