Ban condemned the "complex" assault on the base in Kidal and recalled that targeting peacekeepers constitutes a war crime.
The latest attacks highlighted the vulnerability of the sprawling arid north of the West African country, where UN peacekeepers and Malian soldiers are struggling in their fight against jihadists who had seized vast swaths of territory in 2012.
UN spokesman Stephane Dujarric said some of the peacekeepers who were killed were from Guinea and that there "may be other nationalities involved."
The raid coincided with a visit to the region by Mahamat Saleh Annadif, the new chief of the UN mission in Mali known as MINUSMA, who began touring the north on Monday.