Kolasinac, who was involved in a clash with Victor Moses, was replaced 20 minutes from the end of the contest, which the Gunners won on penalties.
Unai Emery admitted after the game the injury was a concern and tests have now confirmed Kolasinac has damaged knee ligaments meaning he'll be out for between 8 to 10 weeks.
After undergoing a scan on Thursday, the club have now confirmed that the full-back will be kept out for between eight and ten weeks because of the problem with his left knee.
Ramsey is in the final year of his current deal at Arsenal and, despite expressing his wishes to stay at the club, is yet to sign a new contract. He is likely to miss at least seven Premier League matches, as well as two Europa League matches.
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Emery said after the game that Ramsey's omission was just a precaution and an update on the clubs website has confirmed the Welsh worldwide is hoping to return to training next week. Continues to be assessed.
Both players will miss Saturday's pre-season friendly against Lazio.
Arsenal open their Premier League campaign at the Emirates next weekend against defending champions Manchester City, before journeying to Chelsea for their first away fixture the following week.