Omar Celik, Turkey's Culture and Tourism Minister, said the project is an attempt at reconciliation between Turkey's Sunni and minority Alawite communities.
"The Family of the Prophet, Najaf, Kerbela, Mecca and Medina are all holy lands of the Islamic world," said Celik.
He added that the ministry plans to increase the number of journeys of this kind and the number of people attending them.
The group will first visit the Iraqi province of Najaf where the fourth Khalif of Islam, Imam Ali, the cousin of the Prophet Muhammad and the first Imam (in Shi'a beliefs), is buried.
The Najaf shrine is the third holiest site for some of the estimated 200 million followers of the Shi'a branch of Islam.
Then they will visit Karbala, where Imam Ali's son, Imam Hussein, was killed together with his 72 followers.
The group will then head to Saudi Arabia's holy cities: Mecca and Medina.