The three men have been identified as: Thurairaja Varatharajah, Thangamuttu Sathyamurthi and V Shanmugarajah.
After the LTTE's defeat, they were detained on accusations that they gave false information about the number of casualties to the media.
Their whereabouts are unknown.
"We call on the Sri Lankan government to release the doctors immediately, and to respect their rights to legal counsel and to receive medical care as well as family visits," Frank Donaghue, who heads Physicians for Human Rights, in the US said.
The Committee to Protect Journalists has called for the doctors to be released.
"This is a chilling example of the intentions of the Sri Lanka government as it pursues its all out military solution in dealing with the [Tigers]," Bob Dietz, the group's Asia programme co-ordinator, said.
The LTTE's defeat has also raised questions over how the government will reach out to the country's Tamil minority.
About 265,000 ethnic Tamils were displaced in the military's recent offensive against the LTTE, and many of them have been sent to overcrowded camps in the country's north.
The European Union has called for an independent inquiry into alleged human-rights violations carried out during the war.
The International Committee of the Red Cross announced it had suspended its distribution of aid to the displaced.
The group earlier complained it had been unable to reach the wounded in the northeastern conflict zone even after victory was declared.
Speaking in the Swiss city of Geneva, Ban Ki-moon, the UN secretary-general, said that any serious allegations of war crimes "should be properly investigated".
"I remain concerned about the welfare and safety of the civilian population," he said.
The UN's main rights body is to hold a special session on Sri Lanka next week.
Under international pressure to reach out to the Tamil minority, Mahinda Rajapakse, Sri Lanka's president, vowed that a political solution to the island's ethnic divisions would be found.
"All should live with equal rights. They should live without any fear or doubt," he said in his victory speech.
"Let us all be united."
He also called upon Sri Lankans, especially Tamils, who fled the country to return and help it rebuild.
"There are no minority communities in this country. There are only two communities, one that loves this country and another that does not," Rajapaksa said.
For his part, Ranil Wickremesinghe, the country's opposition leader, who the government has criticised for his conciliatory approach towards the Tamils, called for national reconciliation.
"We have to have a discussion among ourselves, among the political leaders who represent the communities, and come up with a new Sri Lankan identity," he said from Brussels.
Rajapakse announced victory over the Tamil Tigers, who had fought for decades for a separate Tamil homeland, on Tuesday.
State television broadcast images of what it said was the body of Velupillai Prabhakaran, the LTTE chief.
The video showed the upper section of a corpse dressed in camouflage fatigues.
The back of the head, which was resting on a bloodstained newspaper, seemed to be missing.
The video appeared to refute an earlier claim by Selvarasa Pathmanathan, the international spokesman for the Tigers, that Prabhakaran was "alive and well".