The Danish world number 11 was leading 6-4, 2-2 against Ugo Humbert when he had to retire from the match, adding to a long list of players who have suffered injuries this season.
"It’s gonna be a while before I can step on court again. It’s tough. I had so much joy on court in Stockholm, and it’s unbearable to think that I will not feel this energy for some time now," Rune posted on Instagram.
"My Achilles is full broken on the proximal part, meaning I need an operation already next week and from here rehabilitation."