"A date has not been set but the trip to Iran will probably be in late April," ministry spokesman Martin Weiss told AFP.
He did not give any other details about the trips.
Iranian media earlier reported that Kurz would be travelling to Tehran on April 26.
Austria has hosted repeated meetings between Iran and the so-called P5+1 world powers -- the United States, Russia, China, Britain, France and Germany -- in the hope of reaching a negotiated deal, and it is also home to the UN atomic watchdog IAEA.