Several allies of former President Amadou Toumani Toure, including former Prime Minister Modibo Sidibe, were arrested by military forces.
Ban, in a statement issued through his spokesman's office, called for the immediate release of those detained by military authorities. The arrests, the statement read, "are in contrast to other welcome developments" in the country.
Dioncounda Traore was sworn in last week as Mali's interim president, more than three weeks after a military coup ended more than 20 years of democratic rule in the West African country.
"The secretary-general calls for the military junta to promptly complete the full transfer of power to civilian rule," the message added.
Authorities had suggested the arrests were a sign Traore didn't have complete control over the country.
Following the coup, Tuareg rebels, who had fought alongside pro-government forces during last year's civil war in Libya, claimed autonomy for northern Mali. The rebel movement is said to be divided between separatist and al-Qaida factions.
Scarlett Johansson steps out with fiance after pregnancy reveal
Dennis Rodman pledges to end trips to North Korea