The killings were the latest in a spate of attacks on foreigners in recent months, police said.
The attack in Potiskum also came just two days after gunmen killed at least 10 people in horrifying attacks on two Nigerian polio clinics in a new blow to the campaign to wipe out disease, but it was not clear if the incidents were related.
Yobe State police commissioner, Sanusi Rufa'i, would not say if the Islamist group Boko Haram, which has been active in Potiskum, was responsible for Sunday's killings, but that the attack was being investigated.
He said unknown attackers scaled the fence of an apartment housing the three doctors at around 1:00 am and slit their throats.
Residents said the Koreans, whose bodies were found by neighbours, were employees of the state ministry of health and had been living in the city for one year.
In Seoul, the foreign ministry said it was checking the reports, but noted that few Koreans live in the town.
"The chance that the slain would be Koreans is not high," a foreign ministry official told Yonhap news agency.
"But we are checking further related situations via diverse channels."
"It is still premature to point any accusing fingers but we have commenced an investigation to unravel the killings," said Mr Rufa'i, adding: "No arrest has been made."
Sunday's attack was the latest in a spate of killings of foreigners, especially Chinese nationals, in the country's restive north east.
Violence linked to Boko Haram is believed to have left some 3,000 people dead since 2009, including killings by the security forces.
Boko Haram has claimed to be fighting for the creation of an Islamic state, but its demands have shifted repeatedly and it is believed to include various factions.
Criminal gangs and imitators are also suspected of carrying out violence under the guise of the group.