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Williams, 26, had returned to pre-season training with the Basque side this week ahead of the new La Liga campaign which begins in mid-September.
"Today it was confirmed that I tested positive after a PCR test. I'm asymptomatic and fortunately I'm doing well. I have to remain isolated now at home to beat the virus," Williams posted on Twitter.
"I can't wait for the moment to arrive so I can join the team for pre-season."
Williams' fellow squad members Oihan Sancet, Unai Lopez and Gaizka Larrazabal also said they were among those to have contracted COVID-19.
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Earlier in the day Bilbao said group training would stop and individuals who tested negative will be examined on Friday.
Elsewhere, Barcelona announced Jean-Clair Todibo had caught the illness but that the defender had not been in contact with the squad travelling to Lisbon for Friday's Champions League quarter-final against Bayern Munich.
On Tuesday, fellow La Liga clubs Valencia and Real Betis as well as second-tier Espanyol and Real Mallorca revealed they had squad members test positive.
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