The decree was read by the Apostolic Nuncio to Croatia, Giorgio Lingua, in this southern town on Saturday.
"With this elevation to the honour of a basilica, the Holy Father wanted to connect the church in Sinj more specifically with the heir of Peter," Lingua said.
Archbishop Zdenko Križić of Split and Makarska said: "The Blessed Virgin Mary, called the Miraculous Lady of Sinj, is at the centre of today's celebration. She is the heart of this parish and without her this church would never be a shrine nor would it be raised to the honour of a minor basilica."
He said that the Miraculous Lady of Sinj attracted pilgrims from throughout Croatia who at this shrine "felt the grace of a mother that heals illnesses and comforts the grieving."
The Mass was attended by Veterans' Minister Tomo Medved, Ivan Bugarin as the representative of the Speaker of the Croatian Parliament and Jadranka Žarković as the representative of the President of the Republic.