The 51-year-old celebrity was accompanied by her four children — her daughters Lourdes and Mercy, and sons Rocco and David.
The official who could not be named because he was not authorized to speak on the matter said Madonna arrived Sunday at about 2:30 p.m. (1230 GMT; 830 EDT) on Ethiopian Airlines.
Madonna adopted the Malawian-born Mercy this year after she adopted David in 2008.
The official said Madonna would take part in a groundbreaking ceremony for the girls school on Monday.
Madonna's Raising Malawi charity helps care for some of the country's 1 million orphans.