The former Bayern Munich coach says the two wingers quarrelled back in 2012 following a dispute over who would take a set-piece
The coach guided the Bavarians to European, Bundesliga and DFB-Pokal glory in 2012-13 and both wingers were key parts in the success, but he says the pair were not always the best of friends.
"Once, [Ribery] was hot under the collar but I told him to stick to the rules and behave himself," Heynckes told France Football, referring to the 2011-12 Champions League semi-final with Real Madrid.
"His argument with Robben was unbelievable. They fought with each other because of a simple free kick!
"There was not this kind of scene again the next season because we learned from our mistakes. After this fight, I made it clear who would take free kicks. And each respected my decision."
Robben risked Ribery's ire again in recent months by claiming that Cristiano Ronaldo deserved the Ballon d'Or over the France international.
The Dutchman also clashed with coach Pep Guardiola earlier in the campaign when he refused to take a penalty following a previous argument over spot-kicks in the autumn.