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.
Purdue officials considered the campus to be secure, said Sands, who in June will become president of Virginia Tech, where an April 2007 campus massacre left 33 dead.
"We're encouraging students to continue about their usual business on the rest of the campus except for the Electrical Engineering Building," he said.
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 the 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.
Cox, the campus police chief, said authorities responded aggressively after the shooting was reported, with about 20 campus and city police officers at the building within minutes.
Sands said the university will offer assistance to those who need it as the circumstances of the shooting are sorted out.