Six dissidents were killed and several Iraqi police officers were wounded when a camp housing Iranian exiles came under mortar attack at the former Camp Liberty, near Baghdad. The facility houses members of the dissident People's Mujahedin of Iran.
A statement from Ban's office said attacks on the dissident community were unacceptable.
"The secretary-general calls on the government of Iraq ... to promptly and fully investigate the incident and bring perpetrators to justice," the statement read.
Baghdad and the United Nations signed a memorandum of understanding in 2011 outlining the voluntary relocation of members of the PMOI from their Camp Ashraf enclave in Diyala province to the former U.S. military base.
U.S. State Department spokeswoman Victoria Nuland condemned the attack on the dissidents.
The United States last year removed the group for its list of foreign terrorist organizations.