Quinn, a New Yorker, was diagnosed with the incurable neurological disease Amyotrophic Lateral Sclerosis (ALS) in 2013.
He died on Sunday morning, his supporters wrote on his official Facebook page. "He was a blessing to us all in so many ways," they said.
The viral campaign has raised $220m (£163m) for ALS research.
The Ice Bucket Challenge did not begin with Quinn, but he and his family and friends helped it become a global social media phenomenon in the summer of 2014.
To complete the challenge, people would dump a bucket of ice water over their heads and post the video to social media, challenging others to do the same or make a donation to ALS research. Often, people did both.
The challenge drew high-profile participants like former President George W Bush, Oprah Winfrey, Lady Gaga and President Donald Trump.