Laurence Soper was arrested and questioned in Italy, where he was living at the time, in 2010 after an alleged victim approached police claiming he had abused him.
He was later released and has not been charged with any crimes.
When British police summoned him again for questioning in 2011 he did not return, sparking what became a five-year Europe-wide manhunt before he was eventually found and arrested in the Kosovan city of Peja earlier this year.
British authorities had requested that he be extradited to the UK, however a Kosovan court blocked the move because under Kosovan law the child abuse allegations against him - some of which date back to the 1970s - had expired.
Laurence Soper was a part of the Benedictine Order, the oldest monastic order in the Catholic Church, taught at St Benedict's School in West London between 1972 and 1984, was abbot of Ealing between 1991 and 2000 and also was a part-time chaplain at Harrow School.
A CPS spokesman said: "We are pleased that the prosecutor in Kosovo has lodged an appeal against the judge's decision in this case.
"The CPS and other agencies continue to do all we can to ensure this individual is extradited following a request by the UK government."