Two people were being held, including the alleged shooter who opened fire with a semiautomatic pistol on Tuesday afternoon at the Hazard Community and Technical College, about 90 miles (145 kms) southeast of Lexington, police said.
Hazard Police Chief Minor Allen told a news conference initial indications were that the shooting was a result of a domestic conflict and there were no signs anyone involved had any connections with the college.
The United States is still on edge about gun violence a month after a lone gunman killed 20 children and six adults at a Connecticut elementary school in a rampage that stunned the nation and has fueled a heated national debate over gun control.
Police described the dead in Hazard as a man in his 50s and a woman in her 20s to early 30s. A female in her teens was injured and taken to the University of Kentucky hospital in Lexington. The identities of the victims and those taken into custody were not being released, police said.
The college president, Steve Griner, told reporters that activities and classes for the school's 4,700 students were being canceled on Wednesday because of the investigation.
The campus was placed under a security lockdown after the shooting, which was lifted later. Police searched campus buildings to ensure everyone was safe.
In a separate shooting in St. Louis, Missouri, a student armed with a pistol opened fire at a downtown college before turning the gun on himself. A school employee struck by gunfire in that shooting was expected to survive, as was the armed student, police said.