The order went into effect on Tuesday as the new academic year began in Swaziland and officials announced that the old textbooks would be replaced with new ones that will only mention the Bible.
The schools were also instructed to submit a list of "qualified religious studies teachers ahead of the start of term," AFP reported.
A top education ministry official, identified in the report as Pat Muir, said primary and high schools would not offer other religions.
The official claimed that the new policy was meant to "avoid confusing pupils" in Swaziland, which reportedly has a Muslim population of about 10 percent.
"At tertiary level they will be able to make a decision to learn about other religions," Muir said.
According to the report, while religious freedoms are included in the country's 2005 constitution, many Swazis mix Christianity with local indigenous beliefs.
Last week, the Education Ministry ordered all head teachers to ensure that the syllabus would not mention any religion other than Christianity, including Islam and Judaism. The small African monarchy has virtually no Jewish population.
The report quoted a Swazi-born Muslim, identified as Sahid Matsebula, who works at a mosque near the capital, Mbabane, as saying that the government's policy may deteriorate religious friction in the landlocked country of only 1.2 million, which has been ruled by King Mswati III, Africa's only remaining absolute monarch, since 1986.
"What plan does the government have in place for our children who are not Christian?" asked Matsebula, adding, "They will be taught one thing at home and taught something else at school."
Swaziland's new education policy comes after "public complaints over Asian and Muslim migration into the country led parliament to set up a commission of inquiry last year," the report added.
As church leaders in the country welcomed the Christianity-only syllabus, President of the Swaziland Conference of Churches Stephen Masilela said, "Christianity is the bedrock religion on which this country was built."