Scotland lock out of Six Nations
Scotland lock out of Six NationsSHARE
The Glasgow forward, capped 33 times by Scotland, was already expected to miss the rest of the year, but he will now be unavailable until mid-March at the earliest.
Glasgow said he had undergone surgery on a finger damaged while playing for Scotland against Samoa last weekend and would be out "for a minimum of four months".
The Six Nations runs from February 3 to March 17.