Government and military sources said that the abduction took place in the city of Bamenda in western Cameroon early on Monday. The students were abducted along with their principal, a teacher and a driver.
"In total, 81 people were kidnapped, including the principal. They were taken to the bush," media outlets quoted a military source as saying.
The government says its forces have launched a massive search operation to find the abductees across the region, Presstv Reported.
"The search for the hostages has been launched - every man has been called in," a government source said.
No one immediately claimed responsibility for the abduction in the violence-hit region where separatists are fighting to form a breakaway state.
The kidnapping - the gravest incident so far in 13 months of unrest - coincides with an upsurge of political tensions in the majority French-speaking country.
In recent months, many people have fled Bamenda and other centers to seek refuge in more peaceful Francophone regions.
The separatist movement gathered pace in 2017 after a government crackdown on peaceful demonstrations.
The separatists have gunned down troops and police, boycotted and torched schools and attacked other perceived symbols of the Cameroonian state.
Authorities have responded with a massive crackdown by police and troops.
According to a toll compiled by non-governmental organizations, at least 400 civilians have been killed this year as well as more than 175 members of security forces.
UN figures show 246,000 people in Cameroon’s Southwest Region have fled their homes, and 25,000 sought shelter in neighboring Nigeria, with many living hand-to-mouth in the forests.
The separatists have imposed curfews and closed down schools as part of their protest against President Paul Biya's French-speaking government.
The central government in Yaounde has rejected calls for secession or a return to Cameroon’s previous federal system of governance. It has tried to reach out to key separatist leaders for political dialogue although nighttime curfews, restrictions on movement, raids and body searches remain in place in Anglophone regions.
The Anglophone community comprise a fifth of the francophone-dominated Cameroon of 22 million people. Its presence is rooted in the colonial past of West Africa and in a decision by France and Britain after World War One to divide Cameroon, a then German colony, under the mandates of the League of Nations.