1580s, Italian title of address or courtesy, equivalent to madam; from c. 1600 as a noun, "an Italian lady," from Italian madonna, from Old Italian ma donna (Italian mia donna) "my lady," from ma "my" + donna "lady," from Latin domina "lady, mistress of the house," from Latin domus "house" (from PIE root *dem- "house, household").
Often specifically "the Virgin Mary," hence the sense of "picture or statue of the Virgin Mary," attested in English by 1640s. The U.S. singer/dancer (full name Madonna Louise Ciccone, b. 1958) attained to pop stardom in the fall of 1984.