The Canadiens say a "minimally invasive" preventive procedure known as endovascular surgery will be used to treat the aneurysms and that Beliveau's health was otherwise "very good."
Beliveau, who turns 80 on Aug. 31, will need a few months to recover from the procedure.
"We are pleased that Mr. Beliveau is under the good care of head team physician David Mulder," Canadiens team owner and CEO Geoff Molson said in a statement. "On behalf of all of our fans, players and the entire Montreal Canadiens family, I would like to wish Mr. Beliveau a prompt and complete recovery."
Beliveau had cardiac problems in 1996 and battled throat cancer in 2000. Last year, he was admitted to hospital for reasons not made public.
The rangy centre had 507 goals and 712 assists in 1,125 games over 20 seasons with the Canadiens — the last 10 as captain. He retired in 1971.
He won 10 Stanley Cups as a player and another seven as an executive with the Canadiens.
The Hart Trophy winner of 1956 and 1964 was inducted to the Hockey Hall of Fame in 1972.
Note to readers: This is a corrected story. A previous version described the surgery as "minimally evasive".