The injury has ruled him out of Palace's trip to Wembley to face Manchester United on May 21 and thrown doubt on his participation in the June 10-July 10 European Championship in France, where Wales have been drawn in Group B alongside England, Russia and Slovakia.
"As far as we are concerned he still has a chance of playing in the Euros. Obviously our cut-off point is May 31," an FAW official told the BBC.
Ledley, who has made 62 appearances for his country, was on Monday named among the 29 players called up by manager Chris Coleman for a pre-tournament training camp in Portugal.
Wales open their campaign against Slovakia in Bordeaux on June 11, before facing England four days later.
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(Reporting by Ian Rodricks in Bengaluru, editing by Nick Mulvenney)
