While the group which oversees Vatican buildings says it will bring in around 30,000 euros, some church leaders claim it will destroy the "architectural traditions" of the area.
Cardinal Elio Sgreccia told local newspaper La Repubblica it was a "perverse decision" to allow the opening.
The restaurant will not occupy any of the famous St Peter's square but church leaders are already unhappy at how the area has become over run by illegal souvenir sellers.
Cardinal Sgreccia is calling for the space to be used to help the poor instead.
A separate Cardinal has called on Pope Francis to intervene.