The young man told CBS Boston he was overcome with emotion when his sister Casey handed him the envelope with the $10 note.
"She kind of explained the backstory and everything, and then it turned into a pretty emotional moment, and [I] started crying," he said.
His sister knew the moment would be a memorable one as Matt and his dad were very close and her brother had always struggled with the loss of his father, particularly on special occasions such as birthdays.
"Him and my dad were so close, and he's had such a hard time anytime that a monumental moment comes up in his life that my dad's not there," she said.
Matt said he has fond memories of going fishing, playing games and riding quad bikes with his dad, before the cancer diagnosis.
"Me and him were just like best friends," he said.
"Anytime we would hang out, it was just like having fun."
His tweet sparked a chord with many other Twitter users who took the opportunity to share their own stories of love and loss.
"My dad passed when I was 13," one person wrote. "What I'd give to simply have a beer [with him]."
"Last year my dad was diagnosed with pancreatic cancer. A few weeks after his diagnosis was my birthday, when he asked what I wanted I told him that I just wanted to share a beer with him because I didn't know if I'd ever get the opportunity to," another person said.