The 23-year-old added a picture of himself to his Instagram stories with his arm in a sling. He included the caption: "Successful surgery. Road to recovery starts now."
The Scottish international suffered a recurrence of the issue he first sustained against AZ Alkmaar in the 3-0 win over Ross County the weekend before last.
Taylor’s absence saw a return of Boli Bolingoli to the starting XI for Sunday’s 1-0 loss at Livingston. The Belgian defender hadn’t featured at all for the Hoops since his infamous substitute appearance against Kilmarnock near the beginning of last season, which saw the postponement of three Celtic matches after it was found he’d flaunted Covid-19 restrictions in the week leading up to the match.