The church has called it its first Ministry and Calling Sunday and hopes it will become a part of its calendar.
It says that a quarter of its current serving clergy are due to retire within the next decade and less than 10% are under 40.
It describes the appeal as a drive to seek and inspire future church leaders.
The church has also begun a five year recruitment drive with a focus on young Anglicans.
The Church in Wales has found it more challenging to recruit people to the priesthood in recent times compared with the 1960s.
Churches across Wales have been invited to take part in the Ministry and Calling Sunday where special readings, reflections and prayers for those thinking about being ordained and for those already being trained for ministry.
The church says it is the first time it has set aside a Sunday to focus on vocations.
The Bishop of St Asaph, Gregory Cameron, who is leading the initiative, said: "The aim of the Ministry and Calling Sunday this year is to invite all members of the church to pray: to pray for vocations, to pray that we may be a church which invites and nurtures vocations.
"We're drawing everyone's attention to the need for vocations, to the need to draw people's attention to the fact that God may be calling them to ordained ministry."
He added: "We remain convinced as a church that the ordained ministry has still got an important role to undertake, and we need to do some work in seeking out vocations - especially among younger people.
Steep decline
"This Sunday comes just at that point of the church's year when the disciples were waiting for the empowering of the Holy Spirit, and we are waiting for God's spirit to renew our church in our own day."
A resource pack for the Ministry and Calling Sunday has been sent to every church.
The BBC's religious correspondent Robert Pigott said the Church in Wales was not the only church to suffering from a decline in clergy.
He said the Roman Catholic church is also facing a steep decline in clergy numbers which is in contrast with the Church of England which says it has no shortage of volunteers largely due to hundreds of women who come forward for training every year.
SIC: BBC