Officials said that old text books were being replaced with new ones that mention only the Bible, and that schools were required to submit a list of qualified religious studies teachers ahead of the start of term.
"Other religions will not be offered at primary and high school level," said Pat Muir, a top education ministry official, adding that the policy sought to avoid confusing pupils.
"At tertiary level they will be able to make a decision to learn about other religions," he said.
Some surveys put Swaziland's Moslem population as high as 10 percent, but the US Department of State in 2015 put the figure at about two percent.
Many Swazis combine Christianity with indigenous beliefs, and religious freedoms are written into the country's 2005 constitution.
The education ministry last week instructed all head teachers to ensure that the syllabus would not mention any religion other than Christianity, including Islam and Judaism.
Sahid Matsebula, a Swazi-born Moslem who works for a mosque near the capital Mbabane, said the government's policy could worsen religious friction in the southern African nation.
"What plan does the government have in place for our children who are not Christian?" he told AFP.
"They will be taught one thing at home and taught something else at school."
The US State Department's International Religious Freedom Report said some schools have long sought to prevent Moslem pupils from leaving early for Friday prayers.
It also said some Christian groups "discriminated against non-Christian religious groups, especially in rural areas where people generally held negative views on Islam."
The new education policy comes after public complaints over Asian and Moslem migration into the country led parliament to set up a commission of enquiry last year.
Some illegal
Church leaders in Swaziland welcomed the Christianity-only syllabus.
"Christianity is the bedrock religion on which this country was built," said Stephen Masilela, president of the Swaziland Conference of Churches.
Swaziland, with a population of about 1.2 million, has been ruled by King Mswati III, Africa's last absolute monarch, since 1986.
The country suffers dire poverty and has struggled to lift its economy, and has faced international criticism that the government stifles dissent, jails its opponents and denies workers' rights.