Edmund, ranked 85, will face a fellow Briton in the quarter-final, his second on the ATP Tour this year. He will play either defending champion Andy Murray or Slovenia-born Aljaz Bedene who meet later.
Mathieu suffered the wrist injury beating Britain's Dan Evans on Wednesday.
It was not clear how serious the injury was.
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(Reporting by Martyn Herman; Editing by Toby Chopra)
