The Welshman went down in the 43rd minute to the concern of Rangers medical staff and after a short period of treatment failed to resolve the issue, the on-loan Juventus man was replaced by Scott Wright.
Ramsey, who had featured on the right of the Rangers midfield for the majority of the goalless first-half, appeared to be holding his hamstring as he made his way into the Hampden Park stands.
The 31-year-old has a torrid record with injuries and only recently began starting matches for Rangers on a more regular basis after initially struggling for game-time following his move from Serie A on January 31.
Ramsey played 80 minutes of the Europa League win over Braga on Thursday that saw Rangers progress to the semi-finals and it would appear playing back-to-back matches in the space of four days has caught up with him.