Premier Markus Soder said crosses should not be seen as religious symbols but as a "clear avowal of our Bavarian identity and Christian values".
"The cross is a fundamental symbol of our Bavarian identity and way of life," Mr Soder said in a statement.
"It stands for elemental values such as charity, human dignity and tolerance."
However, opponents of the ruling Christian Social Union (CSU) believe Mr Soder's move is politically motivated ahead of the state's October elections.
Florian Streibl, parliamentary executive director of the Free Voters told Süddeutsche Zeitung newspaper: "I have to say that the cross is too good to be exploited here for partisan games."
Meanwhile, Jan Korte, leader of the Left party's parliamentary group in the federal parliament, said: "Why can the CSU never think of anything that brings people together, instead of trying to divide the country at every level?"
Premier Markus Söder has denied that the law, which comes into effect on 1st June, ignores constitutional rules on religious neutrality.
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