Parry replaces David Partridge who picked up a groin injury while playing for Orient on the weekend.
Jason Koumas has withdrawn from the squad.
A Football Association of Wales spokesperson said: ''Jason has spoken to us and it has been decided he won't come down for this game because of his personal circumstances.''
City have two representatives in the U21 sqaud for Wednesday's match against Israel. The youngsters are playing in Waalwijk, Holland. A neutral venue chosen by Uefa becuase of the ongoing conflict in the Middle East.
Wales: Paul Jones (QPR), Danny Coyne (Burnley), Jason Brown (Blackburn); James Collins (West Ham), Mark Delaney (Aston Villa), Richard Duffy (Portsmouth), Rob Edwards (Wolves), Danny Gabbidon (West Ham), Lewin Nyatanga (Derby), Sam Ricketts (Hull); Simon Davies (Everton), Carl Fletcher (Crystal Palace), Paul Parry (Cardiff), Joe Ledley (Cardiff), Carl Robinson (Norwich), David Vaughan (Crewe); Craig Bellamy (Liverpool), David Cotterill (Bristol City), Rob Earnshaw (Norwich), Ryan Giggs (Manchester United).
Bulgaria: Georgi Petkov (Levski Sofia), Dimitar Ivankov (Kayserispor/TUR); Stanislav Angelov (Levski Sofia), Igor Tomasic (Levski Sofia), Mihail Venkov (Litex Lovech), Rosen Kirilov (Litex Lovech), Yordan Todorov (CSKA Sofia), Radostin Kishishev (Charlton/ENG); Lucio Wagner (Levski Sofia), Georgi Iliev (CSKA Sofia), Stilian Petrov (Celtic/SCO), Martin Petrov (Atletico Madrid/ESP), Zdravko Lazarov (Erciyesspor Kayseri/TUR), Blagoy Georgiev (Red Star Belgrade/SCG), Georgi Peev (Dnipro Dnipopetrovsk/UKR); Dimitar Berbatov (Tottenham Hotspurs/ENG), Svetoslav Todorov (Portsmouth/ENG), Zoran Jankovic (Dalian Shide/CHI).
Wales Under-21 squad to face Israel (Uefa U21 Championship, Waalwijk, Holland, 16 August): Price (Ipswich), Hennessey (Wolves); Adams (Bury), Blake (Cardiff), Critchell (Southampton), Davies (Cambridge), Jacobson (Cardiff), Eardley (Oldham), Morgan (MK Dons), Mike Williams (Wrexham); Crofts (Gillingham), A Davies (Yeovil), Edwards (Shrewsbury), Collins (Fulham), MacDonald (Swansea), Marc Williams (Wrexham); C Davies (Verona - on loan at Wolves), D Williams (Yeovil).