Mattias Tesfaye, the party's spokesman on vocational education, told the Jyllands-Posten newspaper that the move was necessary to prevent young Danes being lured into practicing Islam.
“Denmark's schools, colleges and universities are not a place for religious practice,” he said, warning of the “danger of prayer-rooms”, which he claimed extremists sometimes used to share radical Islamist literature.
“There may be social control in which some Muslim students, for example, push others to practice Islam in school,” he argued.
The move sees the country's largest centre-left party deepen its tentative alliance with the populist, anti-immigrant Danish People's Party, which proposed the prayer ban.
The measure is clearly aimed at devout Muslims, who unlike Christians, Jews and other religions are required to pray five times a day.
However, the Social Democrats stopped short of voting for the measure on its first reading in the Danish parliament on Tuesday, arguing that the proposals needs to be fleshed out and debated before it can make a decision.
The issue also appears to have split the party with Daniel Toft Jacobsen, its spokesman for free schools, saying he disagreed with the decision to back the ban. "For me it's a pretty fundamental question, so I choose to say what I mean," he told Jyllands-Posten. "It has to do with basic values of freedom."
The two Danish government parties, the Liberal Party and the Liberal Alliance, argue that while praying in schools should be discouraged, it is not necessary to ban it under law.
Education Minister Merethe Riis Ager plans instead to send a letter to the leaders of Danish educational institutions encouraging them to ban prayer rooms.
The proposals was universally condemned by Denmark's religious leaders, with representatives for Jewish, Catholic, and Protestant communities saying it was against Danish culture.
“It is dangerous to try to restrict people's freedom to practice their religion,” said Denmark's chief rabbi Jair Melchior.
“It is a freedom that not only the Danish, but the entire of Western society is built upon.”
"It is an expression of religious freedom that you also respect other religions and their needs,” said Niels Messerschmidt, Information Officer of the Catholic Church. “So if Muslims at Danish universities want to ask for prayer spaces, then we support it.”
Henrik Stubkjær, Bishop of Viborg, said it was necessary “in the name of freedom” for there to be places where those of different faiths can pray.
The DPP claims that prayer rooms are working to “Islamize Denmark"
“Denmark is a Christian country, so educational institutions must make sure there is no Islamization,” the DPP's education spokesperson Marie Krarup has claimed.