Father Martin Xavier Vazhachira had served at St John The Baptist Roman Catholic Church in Corstorphine, Edinburgh, since last year.
His body was found on the beach at Dunbar on Friday afternoon. The cause of death has yet to be established.
Father Vazhachira, 33, was originally from India.
Archbishop of St Andrews & Edinburgh Leo Cushley led the service. About 200 people attended.
The archbishop said of those attending mass: "They're bewildered and saddened by what has happened."
He said they would miss their priest greatly, adding: "He was a very kind and gentle man and people here had grown very affectionate and fond of him already in this short space of time so they really don't know what to make of it.