The barrier near Moschendorf, one of a number of government measures meant to be completed by June, is set to be several kilometres long but crosses two Church-owned properties.
A fence "would contradict the spirit of the Gospel, Pope Francis's clear message to Europe, and in particular for a diocese that was in the shadow of the Iron Curtain for decades," said Aegidius Zsifkokvics, bishop of Eisenstadt.
"Last year, during the worst refugee crisis of recent years when 200,000 people crossed the border at (nearby) Nickelsdorf in six weeks, practically overnight we provided around a thousand emergency places in Church buildings for exhausted families, for women, children and old and weak people," he said.
"And now we are supposed to build a fence on Church lands?," he said. "We need to tackle today's problems at their root and that means: stopping organised human trafficking, stopping sales of European arms, stopping war and the deliberate destabilisation of the Middle East and stopping the exploitation of African raw materials and agriculture by European firms," he
Austria last year received 90,000 asylum seekers and saw around 10 times that number transit through the country, mostly towards Germany and Scandinavia, after trekking up from Greece through the western Balkans.
Under Austrian pressure, countries in the Balkans earlier this year effectively shut down this route and Vienna plans to erect several barriers, including at Moschendorf and at the Brenner Pass on the Italian border, in case of a new influx.
The permanent controls on its eastern border will be introduced from Monday in an attempt to slow the number of asylum seekers.
Zsifkokvics added that a fence would also be in clear contradiction to the pope's Year of Mercy.