Rahmani Fazli was welcomed by al-Araji and Iranian Ambassador Iraj Masjedi at Baghdad airport, IRNA reported.
The two ministers were scheduled to sign a memorandum of understanding on Arbaeen rituals.
Also on Wednesday, Parliament Speaker Ali Larijani departed for Russia to take part in a high-level inter-parliamentary commission meeting.
Larijani is scheduled to hold bilateral talks with his Russian counterpart in a meeting attended by parliamentarians from both countries.