The 34-year-old joined La Real on a free transfer earlier this month but returned a positive Covid-19 test after arriving to San Sebastian.
The Liga club said it was Silva’s second test within 72 hours since landing in Spain, having previously tested negative.
The Spaniard, a former World Cup and European Championship winner, left Man City at the end of his contract before signing a two-year deal with Sociedad.
He is self-isolating and is displaying no symptoms, the club said.
Silva’s new teammate Mikel Oyarzabal has also contracted the virus and was replaced in Luis Enrique’s Spain squad by Villarreal forward Gerard Moreno.
Spain face Germany in their Nations League opener in Stuttgart on Thursday, before hosting Ukraine three days later.
The 2020/21 La Liga campaign gets underway on September 12.
