The pupils, aged 10 to 14, were abducted from a Presbyterian secondary school near Bamenda, capital of the restive western region.
24 hours after the abduction, survivors say that armed men broke into the facility in the early hours of Monday morning.
A video purporting to show the kidnapped students was posted on social media from a group of men who call themselves "Amba boys", a reference to the state of Ambazonia that armed separatists want to establish in Cameroon's Anglophone North West and South West regions.
Local governor Adolphe Lele L'Afrique Tchoffo Deben placed the blame on local English separatist militias, though no one group has claimed responsibility at this point.
At least 78 schoolchildren and their head teacher have been kidnapped in Cameroon by separatists fighting for an English-speaking homeland.
"In total 81 people were kidnapped including the [school] principal".
The separatists in Cameroon have been protesting against the French-speaking government led by president Paul Biya and demanding a separate state. The children also say that armed men kidnapped them Sunday night and that they do not know where they are being held.
In the video, the kidnappers force several young male students to give their names and the names of their parents.
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Meanwhile government has accused separatists who are now fighting an armed campaign for independence in the English speaking side of the country where the kidnappings occurred. The video could not be independently verified, but parents said on social media they recognised their children in the recording.
"We hope and pray they release the kids and the teachers", he added. Biya, who has been in office since 1982, is set to be inaugurated tomorrow.
Mr Biya was credited with 71.3pc of the vote, although the ballot was marred by allegations of widespread fraud, low voter turnout and violence.
Around a fifth of Cameroon's 22m people are English-speaking - a minority whose presence dates back to the colonial period.
Cameroon, once a German colony, was divided between Britain and France after World War I.
The children were taken from a Presbyterian school near the city of Bamenda, which is at the center of an Anglophone separatist movement.
They have decreed a boycott of schools, saying that the French-speaking education system marginalises anglophone students.
At least 400 civilians and more than 175 members of the security forces have been killed in the year to September, according to a toll compiled by non-governmental organisations.