The 86-year-old was cast to portray Ser Denys Mallister, an elderly member of the Night's Watch military order, and began filming scenes in the HBO series last week. He died on Friday at his home.
Friends and family attended the service at St Brigid's Catholic church in his native city of Belfast.
Fr Edward O'Donnell said: "JJ knew from his earliest days in the old Group Theatre what his path in life was to be and so all he did in the theatre was a labour of love."
The thespian's film credits include Cal (1984), Angela's Ashes (1999) and Mickybo and Me (2004).
He has a character role in the forthcoming film Dracula Untold and, just days before his death, filmed his first scenes for Game of Thrones, also shot in Northern Ireland.
JJ Murphy trained with the Ulster Group Theatre and worked for many years at the Lyric Theatre in Belfast, where he helped mentor a younger generation of local actors including Ciaran Hinds and Liam Neeson.
Fr O'Donnell said the actor had continued to play an active part in the life of the congregation.
He added: "His sudden death, therefore, comes as a great shock to us all and even more so for the love of his life, Mary."
He had a son Joe, daughter Jane and granddaughter Sarah-Jane.