According to an official from the local Catholic diocese, Fr Antonio Cesar Fernández was returning from a meeting in neighbouring Togo when his car was ambushed last Friday.
Fr Jacob Lompo, bursar of Fada N'Gourma Diocese, told the Catholic charity Aid to the Church in Need: "The armed men stopped the vehicle and forced the passengers to disembark.
"Then they took the priest to one side and shot him in the head."
It is alleged Fr Antonio, a missionary from Spain, was killed by a group who had recently murdered four policemen and burned down a customs check point.
Two other people travelling with the 72-year-old escaped unharmed.
Fr Jacob said the killing has stoked fears among local Christians already on alert against the growing threat posed by extremism.
He added: "A number of communities and churches have been forced to close down because jihadist groups have been going through the villages threatening the inhabitants and demanding that they convert to Islam."
"Many of the Christians are terrified and have fled."
Friday's killing is unusual in the south of Burkina Faso as activity by Islamic extremists has tended to take place in northern and eastern areas.
Militia groups including Ansar ul Islam and JNIM (the Group to Support Islam and Muslims) are known to be active in the west African nation.
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