Wright has decided to concentrate on events at McDiarmid Park after succeeding Steve Lomas, who quit the club to join Millwall last week.
The decision was taken after talks with Saints chairman Steve Brown and Northern Ireland boss Michael O'Neill.
Wright said in a statement on the Irish Football Association website: "Following discussions with my chairman, Michael O'Neill and my family I have decided to step down from the position of Northern Ireland goalkeeping coach.
"The decision was not taken lightly but I feel that the demands of being manager of St Johnstone FC require me to be totally committed to that position.
"I would like to thank the chairman and board of directors at the club for allowing me to work with the international team over the past 15 months and it has been a position that I have been honoured to hold.
"Finally, I would like thank Michael for the opportunity to work alongside him and Billy (McKinlay) and I wish them and the squad all the best for the remainder of the World Cup campaign."