The left-back was forced off shortly before half-time of the game at Anfield due to an ankle injury and posted an update on social media on Monday evening.
Robertson wrote: “Thanks to everyone for the kind messages and support. Scan suggests nothing too major but there’s some ligament damage which will need to mend. I will be grafting every day so I can help the team again sooner rather than later. Good luck to the boys playing tonight #YNWA.”