Purdue Police Chief John Cox said the suspect appeared to have targeted the male victim in a basement classroom of the Electrical Engineering Building about noon and didn't attack anyone else.
"The individual entered the facility and took the actions that he took, and then immediately left the facility without any other interaction that we're aware of," Cox said.
The suspect gave himself up to a West Lafayette police officer outside the building on the 40,000-student campus, he said.
Cox and Purdue Provost Tim Sands told reporters during an afternoon news conference that they had not yet confirmed the identities of either the suspected gunman or the victim.
Cox said the man arrested wasn't immediately cooperating with investigators.
Purdue officials issued a text alert telling those on the campus about 60 miles northwest of Indianapolis to seek shelter shortly after the shooting was reported. Within two hours, the university said there was no ongoing threat on campus and allowed normal operations to resume in all buildings except the engineering facility.
Students described a chaotic scene when the first report came in.
Julissa Martinez, a freshman nursing student from Portage, said she was in psychology class on another part of campus when she received the text message saying the university was on lockdown. She said her professor briefly kept teaching, then stopped lecturing so that students could contact people to let them know they were safe.
"He tried to get everything under control because people were freaking out," she said.
She said students were nervous because there was a lot of speculation about the severity of the situation.
"It was scary because you hear about it, but you never expect it to happen on your campus," Martinez said.
Senior Saran Mishra, editor of the Purdue Exponent, the campus newspaper, said some students reported hearing fire alarms and were told to evacuate.
"Right now I'm still in shock," he said.
Associated Press writers Tom Coyne in South Bend and Jeni O'Malley and Tom Davies in Indianapolis contributed to this report.