Staff Sgt. Jeff Johnston says 71-year-old Yvon Arsenault of Aldouane is also charged with three counts of indecent assault and four counts of gross indecency.
Police say the alleged incidents occurred in Shediac, Rosaireville and Collette and involved four boys under the age of 18.
RCMP began investigating last December after receiving a complaint.
That same month, the Archdiocese of Moncton confirmed that Arsenault had been ordered six months earlier not to carry out any duties as a priest after it became aware of abuse allegations.
The Mounties say they believe there are other alleged incidents involving Arsenault and their investigation is ongoing.
Arsenault is due in Moncton provincial court on January 27.