Ledley, part of Wales manager Chris Coleman`s provisional squad for France, replaced Yohan Cabaye for the second half but limped off 11 minutes later.
Wales name their final squad on 31 May.
An FAW spokesperson said: "As far as we are concerned he still has a chance of playing in the Euros. Obviously our cut-off point is 31 May."
It is exactly a month until Wales play Slovakia in their opening game of Euro 2016 on 11 June, before a match against England five days later.
A Crystal Palace statement confirmed that Ledley had suffered a fracture of the fibula, adding "he will be continually assessed over the next few weeks by the club`s medical staff".
Palace travel to Southampton for their final Premier League game on Sunday before facing Manchester United in the FA Cup final at Wembley on 21 May.
Ledley, a former Celtic player, was part of the Cardiff City side beaten 1-0 by Portsmouth in the 2008 FA Cup final.
It would be a significant blow to Coleman if Ledley was missing from his Euro 2016 squad, as Wales prepare for their first major international football tournament since 1958.
He played an integral part in qualifying for France, featuring in seven of the 10 Group B games, and offers valuable experience to the Welsh midfield.
Wales will travel to Portugal for a pre-tournament training camp on 23 May.
After the final squad announcement, Wales play Sweden away on 5 June, their last friendly before Euro 2016.
After games against Slovakia and England, Coleman`s side then face Russia in their final Group B game on Monday, 20 June.
