Reynolds, 52, led Canaccord Genuity as it was transformed from a Canadian brokerage business to an independent global investment bank.
He is survived by his wife and four children.
Reynolds is the son of former federal West Vancouver MP John Reynolds, who also served as an member in the British Columbia legislature.
John Reynolds said in an email that Paul was the oldest child and had six brothers and sisters.
He said the entire family was in Hawaii.
Paul Reynolds was competing Sunday in the Lavaman Waikoloa Triathlon in Kona, Hawaii, that includes a 1,500-metre swim, 40-km bike ride and 10-km run. According to media reports, he ran into problems during the swim and was pulled from the water and rushed to hospital.
Canaccord said Thursday its chairman, David Kassie, has been appointed to fill the chief executive's role immediately. He will help with a search for a permanent successor.
"This is a difficult day for everyone at Canaccord Genuity," Kassie said in statement.
"As the architect of our firm's global transformation, Paul's distinct style of partnership, friendship and respect over three decades of commitment is just part of the legacy he leaves us all."
Canaccord Genuity said it wasn't planning further comment at this time. It also said the family had requested privacy.
Canaccord Genuity is one of Canada's largest non-bank investment and capital markets firms, currently operating offices in 10 countries including the United States. Its main Canadian offices are in Vancouver and Toronto.