"We had a problem with Roberto in the last match," Silva told reporters on Thursday. "He's out for Saturday."
Silva said he was hopeful Pereyra would recover in time for next week's game against Everton.
"He will be a big miss to us, just like some of the others. He came in, did very well in the last game again and we hope if not for the next match then after the break he is available."
Pereyra was restricted to six league appearances in the last campaign after sustaining a season-ending knee injury in December.
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Watford defenders Younes Kaboul and Sebastian Prödl, who picked up hamstring injuries last month, are expected to return to full training within the next week.
Fellow defender Craig Cathcart, forward Isaac Success and midfiedler Nathaniel Chalobah have yet to recover from long-term knee injuries.
Watford, sixth in the league, have lost their last three league matches against Stoke, who are currently 17th.
(Reporting by Aditi Prakash in Bengaluru; Editing by Peter Rutherford)
