The shooting rocked the campus of Hazard Community and Technical College in the early evening, police told reporters at a news conference streamed online by local television station WYMT.
"It was not related to the school in any way," Hazard police chief Minor Allen said. "We think it was a domestic-type case."
The victims were described as a man in his 50s and a 20-year-old woman. A teenage girl was injured and taken to hospital for treatment.
Police identified the gunman as Dalton Stidham, 21, who turned himself in to authorities. A lockdown was ordered for about two hours at the school, they added.
The college, which operates at several locations, cancelled classes for Wednesday on the campus where the incident took place.
The United States is once again in the midst of a heated debate about how to put a stop to gun violence, following last month's shooting rampage at an elementary school in Connecticut that left 20 children and six adults dead.
On Wednesday, President Barack Obama is expected to call for universal background checks for gun buyers, an assault weapons ban and limits on high-capacity magazines, following a policy review by Vice President Joe Biden.
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