The bylaw pushed through by Markus Söder, the Bavarian state premier, requires government buildings to display a cross in their entrance from next month.
Cardinal Reinhard Marx, head of the German Bishops' Conference, told the Süddeutsche Zeitung that Mr Söder had not discussed the law change with him and warned against "instrumentalising" the Christian symbol.
"This has caused unrest and is pitting people against each other," Cardinal Marx said.
Mr Söder said in a statement that the cross "stands for elemental values such as charity, human dignity and tolerance".
He added that crosses should not be seen as religious symbols but as a "clear avowal of our Bavarian identity and Christian values".
Roman Catholic and evangelical Christian leaders have also said they are concerned the cross is being used by the ruling Christian Social Union as nothing more than a political tool to garner votes ahead of October's election amid fears of a rise of the far right.
The order could still be challenged in the courts for breaching the German constitution's insistence of equal treatment of religions.