The ship was participating in a military exercise in the waters off the port of Jask in the Gulf of Oman.
Of those 15 people, 12 were hospitalized and three more, with minor injuries, received medical assistance.
"The circumstances of the incident are currently under technical examination," Iranian Students News Agency reported.
Reports tonight that an Iranian Navy Moudge Class Frigate has opened fire on an Iranian Navy vessel called “Konarak” in a friendly fire incident near Jask. Reports of at least 20 dead. #Iranpic.twitter.com/3TkNHcVeEL
The Konarak was accidentally sunk by an anti-ship missile, fired from another Iranian Navy ship. As a result, all crew members were killed, according to sources.
That Hendijan-class support ship was too close to a target during the exercises.
The ship Jamaran, operated by Iran's Islamic Revolutionary Guard Corps, reportedly fired the missile prematurely before Konarak had time to sail away from a floating target that had been towed to a designated position.