Orlando Police Chief John Mina declined to release the name of the suspect pending further investigation, but said that he had come from another — unidentified — Florida city to kill Grimmie.
"He came here to commit this crime and had plans to travel back to where he came from," Mina said.
He said detectives were attempting to get information from the suspect's phone and had not yet established a motive for the killing. He said detectives were en route to the suspect's home city to search his residence.
Mina indicated that the suspect planned to leave Orlando by some form of public transportation, such as plane, train or bus.
"There is is no car that we are looking for," Mina said. "He did make travel arrangements to get back where he was going."
Police said the the suspect was carrying two handguns, additional ammunition and a large hunting knife.
The shooting occurred near the back of the venue around 10 p.m. while Grimmie was hosting a meet-and-greet for fans.
Mina said the gunman "approached her and opened fire, striking her."
The police chief said the club looks in the bags of concertgoers when they arrive, but does not have a metal detector.