The 34-year-old joined La Real on a free transfer earlier this month but returned a positive Covid-19 test after arriving at 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.
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.