The loss at Holy Trinity in Torbryan took place sometime between July 22 and August 8 and the Churches Conservation Trust (CCT) is asking dealers and auction houses to be on the look-out for any sign of the panels, showing St Victor of Marseilles and St Margaret of Antioch.
A third panel of a female saint was also damaged, and CCT - the national charity protecting historic churches at risk - said the theft of the c.1460-70 designs was a "great blow to the church".
The oak screen represents a variety of saints and church dignitaries. The CCT stated: "The artistry is of a very high status, suggesting that the artist was specially commissioned to produce the panels for the screen.
"Even though some of the panels have been missing for many years, the Torbryan screen represents an exceptionally complete survival from the late medieval period that escaped the worst excesses of the iconoclasts who took down most of the screens in the country during the Reformation, especially those that included representations of saints".
CCT chief executive Crispin Truman said: "I was shocked to learn of the theft of these panels and the damage done to this significant art work. Holy Trinity is a beautiful public building much admired around the country and beyond, and this crime will deprive all visitors and researchers of an important part of Devon heritage and is essentially a theft of public property. We hope that by publicising the loss we might be able to recover the panels."
Holy Trinity has been in the care of CCT since 1987, and is looked after by a small volunteer team who live locally and help the organisation to open, clean and care for the church.
Other panels from the screen were also stolen in 2003 and are unrecovered.
ATG reported on a spate of church thefts last year, mostly from the Oxfordshire, Herefordshire and Warwickshire area.