There was no immediate word about how serious the injury was.
At 81 in the ATP standings, Darcis is Belgium's second-highest ranked player behind world number 16 David Goffin.
Darcis, who once beat Rafa Nadal at Wimbledon, won the deciding rubber against Argentina in a thrilling semi-final, beating Federico Delbonis.
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Belgium are in the Davis Cup final for the first time since 1904 when they lost to Britain. They were also in the semi-finals in 1999.
(Reporting by Martyn Herman; editing by Toby Davis)
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