The former Aston Villa and Wolves keeper died suddenly on Saturday morning. He was 26.
English-born, Sarkic earned nine caps with Montenegro, with the Federation stating:
"With immense sadness we received the news that our dear Matija Šarkić left us at the age of 27. On this difficult day, our thoughts go out to your family, relatives, friends, teammates and all those who shared the joys of life with you.
"We will miss you, our dear Matija. We will miss your cheerful spirit, your work ethic, your presence in goal, your great defenses... Most of all, we will miss the human greatness of Matija Šarkić. May the angels watch over you just as you have watched over all of us.
"We are deeply saddened by the tragic loss of our beloved Matija Šarkić. Matija was not only an extraordinary athlete, but also a dear teammate and friend. He was the present and the future of our national team. His unexpected death has left us all shocked and saddened.
"Our thoughts and deepest condolences go out to the family, friends and teammates of Matija Šarkić. This is an incredibly difficult time and we kindly ask for respect and privacy for his loved ones as they grieve this unimaginable loss."