A nationwide search is continuing for Revd Simon Reynolds who failed to return to court on Thursday to hear a jury find him guilty of four counts of theft.
South Yorkshire Police said it was working with forces across the country to find the 50-year-old.
Reynolds, was convicted of keeping around £24,000 of fees given to him for weddings, funerals and graveyard memorials when he was priest-in-charge of All Saints Church in Darton, near Barnsley.
The Church of England vicar left Sheffield Crown Court at lunchtime and did not return.
A warrant was issued for his arrest and officers are actively searching for him, police said.
A South Yorkshire Police spokeswoman said: "We are working with a number of forces across the country to find him.
"We are urging people who may have seen him to phone 101."
Reynolds went on trial last week accused of keeping fees handed over to him by bereaved families and engaged couples.
He should have handed over the money to the diocese and the parochial church council, the court heard.
The offences were described as a "significant breach of trust".
South Yorkshire Police is asking anyone who may have seen Reynolds to contact 101 quoting incident number 864 of July 23 2015.
A Joint statement from the Diocese of West Yorkshire and the Dales and the Diocese of Guildford expressed concern for the well-being of Reynolds.
It added: "We ask people to keep Simon and his family in their prayers and urge him to get in touch to allow justice to take its course."
The Archdeacon of Pontefract, the Ven. Peter Townley, said: "Our thoughts and prayers are with all of those affected by this crime.
"We deeply regret any further pain caused to those families who paid fees to Simon for funerals and our hope is that this conviction now affords some peace.
"The consequences of Simon's actions have been felt far and wide, not least by parishioners here in Darton but also in Farnham, Surrey, to where he moved in March 2013.
"It is of course a matter of deep disappointment when a member of clergy acts in anything other than an exemplary manner.
"Simon, as with all other members of clergy, received training and advice on how to handle all fees paid to him directly and the court has found that he knowingly flouted this advice and kept the money for himself."