He replaces Mohammad Saeedi after the latter handed in his resignation, Mehr News Agency reported.
The reason for the resignation was not announced.
Khiyabani has been a board member of IRISL until his Sunday appointment, Financial Tribune reported.
Mohammad Saeedi had been serving as the managing director of IRISL Group since August 2015. He succeeded Mohammad Hossein Dajmar, who had held the position for 10 years.
The maritime fleet of the Islamic Republic of Iran Shipping Lines, which is Iran's biggest shipping operator, comprises 115 ocean-going vessels, with a total capacity of 3.3 million tons deadweight.