Strydom - who played as a lock - represented the Springboks on 21 occasions between 1993 and 1997 and played every minute of his nation's 1995 World Cup final victory over New Zealand.
During a 14-year club career, Strydom - who also worked as a pharmacist - turned out for Eastern Province Elephants, Northern Transvaal (Blue Bulls) and the Golden Lions, and he was also involved in South Africa's Test series against the British & Irish Lions in 1997.
"Hannes was one of the great locks of his generation and as a member of the Springbok squad from 1995, one of the heroes of our local game," SA Rugby president Mark Alexander said in a statement.
"He also played more than 100 games for the Lions at a time when they dominated the game in South Africa and won the Super 10 before it became Super Rugby, which underlined the quality of that team.
"Hannes, along with other players from that Lions team, such as Francois Pienaar, Balie Swart, Kobus Wiese, and Hennie le Roux, formed the core of the famous Bok squad that lifted the Webb Ellis Cup in South Africa in 1995.
"He was a hard-working lock who never shied away from getting stuck in and doing the dirty work. To lose yet another member of the iconic Bok squad from 1995 is a heavy blow to the rugby fraternity here in South Africa and our thoughts and condolences are with his wife, Nikolie, their children, Annalie, Hannes and Lucy, family and friends in this very difficult time."