His coach Thierry Van Cleemput said the in-form Goffin, ranked 12th in the world, had not suffered a ligament tear but more time would be needed to determine the length of his absence and whether he would play during the grass season.
"There is no tearing of the ligaments and no bone that's been broken, either," said Van Cleemput. "We know there is nothing serious due to which he wouldn't be able to play for a long period of time."
"But as we speak, we cannot tell you when he's up and running again and when he can play tennis."
"Will he play on grass? I don't know. I can't answer this question."
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Wimbledon, the year's third grand slam, starts on July 3.
Goffin was leading 5-4 in the first set when Zeballos, who had earned his first break point, forced him to the edge of the court near a cover with a deep groundstroke.
Goffin, a semi-finalist in Monte Carlo this year, managed to get to the ball, lifting a lob over the Argentine, but slipped and hurt his ankle.
Medical staff rushed on and helped him off court for a medical check before the umpire announced minutes later that the 26-year-old had been forced to retire.
Zeballos, 32, who is in the fourth round at Roland Garros for the first time, will play sixth seed Dominic Thiem of Austria who beat American Steve Johnson on Friday.
(Reporting by Karolos Grohmann, editing by Julien Pretot and Ken Ferris)
