In the course of the visit, Al-Thani is expected to hold talks with Iran's newly-appointed foreign minister, Abbas Araghchi, the agency said.
The parties will reportedly discuss the relations between Doha and Tehran, also touching upon key regional issues.
Last week, Doha hosted Gaza ceasefire talks involving Qatar, Egypt, the United States and Israel. Palestinian movement Hamas refused to attend, citing the lack of specifics on the terms of the truce.
After the talks, the US, Egypt and Qatar said in a joint statement that their mediators had presented to both parties a bridging proposal on a ceasefire and the release of hostages based on the relevant UN Security Council resolution and the principles laid out by US President Joe Biden in May.