Ayguel Oezkan, the 38-year-old daughter of Turkish immigrants, is poised to become social minister in the centre-right government of the western state of Lower Saxony, and called for the ban in an interview with a German magazine.
'Christian symbols do not belong in state schools,' she told weekly Focus last week. 'Schools should be a neutral place.'
Members of her party, the Christian Democratic Union (CDU) of Chancellor Angela Merkel, have been quick to denounce the comments and some are demanding she renounce her regional minister role, which she is due to assume tomorrow.
Lower Saxony state premier Christian Wulff, an ally of Ms Merkel who won praise last week for appointing Ms Oezkan to his cabinet, brushed aside her comments as 'personal opinion' and reaffirmed that his government welcomed crosses in schools.
Stefan Mueller, a member of parliament who represents Angela Merkel's CDU and its Bavarian Christian Social Union (CSU) allies on integration issues, used stronger language, calling the remarks 'absurd and shocking'.
'Politicians who want to ban crosses in schools should think about whether they belong in a Christian party,' Mr Mueller was quoted as saying in German media.
Ms Oezkan, a lawyer who was born in Hamburg to parents who migrated to Germany in the 1960s, said in an interview with German daily Bild that she did not consider herself a devout Muslim but that her family celebrated Islamic holidays.
Ms Oezkan, who would be the first state minister of Turkish origin in Germany, told the paper she had received death threats.
She is reportedly under 24-hour protection from police.
Germany is home to nearly 3m people of Turkish origin, many of whom came to the country as 'Gastarbeiter', or guest workers, in the decades after WWII.
Ms Merkel's government has tried to address perceived problems in integrating the country's Muslim population with a series of so-called 'integration summits'.