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.
The 51-year-old celebrity was accompanied by her four children - her daughters Lourdes and Mercy, and sons Rocco and David.
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.