Rinaldi, who had been on loan at fourth-tier side A.C. Legnano, was described by Atalanta as a “positive” personality and “well-liked by everyone.”
A.C. Legnano said in a statement on its website that Rinaldi’s death had been caused by an aneurysm.
“In the prime of his years, with a life ahead and a career that promised bright goals … sudden and shocking tragedy, impossible even to imagine,” the club said.
In its statement, Serie A club Atalanta said: “Just as on the pitch you were always the last to surrender, this time too you fought with all your might not to fly away too soon.
“But that kind smile of yours will always remain alive in the heart of those who have had the good fortune to meet you.”
Rinaldi joined Atalanta as a 13-year-old and helped the club win the under-17 league title and Supercup in 2016.
Legnano president Giovanni Munafò added: “Andrea was coming to the training session and the first thing that he would do was to come to me and say, ‘Hi.’
“This is a memory that I will carry in my heart. An extraordinary boy, an example to everyone.
“On behalf of the club, I express my most heartfelt condolences to the family. We’re sure that Andrea from up there will be the warrior he used to be here, fighting in the pitch to bring joy to the Legnano fans.”