Its parent company Edinburgh Crystal and sister firm Caithness Glass have already gone into administration.
Local politicians, who held talks over the firm's future only days ago, have expressed shock at the move.
"This is extremely bad news, first and foremost for the staff who have worked very hard at Selkirk Glass to make it the well-respected company that it is," said Lib Dem MSP Jeremy Purvis.
He said he had been hopeful that the company could have survived this "period of uncertainty".
"I have been saying that there have been unacceptable question marks hanging over the Selkirk company.
"I have been informed that yesterday afternoon the directors of Edinburgh Crystal put Selkirk Glass into administration and the administrators had made the decision last night to close it.
"The reasons I have been given have been poor retail sales and the catering, that has been excellent there, has not been making money."
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Borders Glass Firm Faces Closure
A Borders glass company has gone into administration, placing a question mark over the future of 34 jobs. Administrator Deloitte is reviewing the financial situation at Selkirk Glass to see if the company can keep trading while a buyer is sought.