Sources connected to the 76-year-old bodybuilder/actor/politician tell TMZ ... Arnold had nerve damage in his elbow that required surgery last Thursday. Doctors put a protective cast on his entire right arm, so Gold's Gym is without its leader ... but probably only for a week.

He got in his last workout just hours before the operation, and now he's getting his exercise by strolling in the SoCal sun.

Arnold released a never-before-seen video last week, revealing his 2018 heart surgery was way more serious than anyone knew. It was supposed to be a routine, non-invasive procedure to replace a heart valve, but something went wrong and doctors quickly decided to do full-blown open-heart surgery.