The three clergymen were stabbed by an unknown assailant in the holy shrine of Imam Reza (AS) on Tuesday afternoon.
A video shows two people suffering stab wounds lying on the ground in an open area of the shrine.
Another video shows pilgrims and security forces catching a man, purported to be the assailant.
The Astan Quds Razavi, a charitable organization holding trusteeship of the holy shrine of Imam Reza (AS), said in a statement that it was investigating the issue and will release a report later.
The holy shrine of Imam Reza (AS) is visited by millions of pilgrims every year, who are frisked at the entrance.