Police chief John Mina said the gunman “travelled to Orlando to commit this crime” but did not appear to know her personally.
Ms Grimmie was shot while signing autographs after a concert in the city on Friday night, and died in hospital.
In 2014, she was a contestant on US TV programme The Voice.
Police say Ms Grimmie was shot about 22:45 local time on Friday (02:45 GMT Saturday) at The Plaza Live in Orlando.
Mr Mina said the gunman, who shot himself dead during a struggle with the singer’s brother, was a 21-year-old white male and had two handguns and a hunting knife. His name has not been released.
“She was doing a meet-and-greet, just signing autographs and selling merchandise,” he said.
“This white male approached her and opened fire, striking her.”
The police chief praised Ms Grimmie’s brother Marcus.
“Very heroic actions by Marcus Grimmie to jump in and it definitely could have prevented further loss of life,” he said.
The singer had been performing with the band Before You Exit.
Up to 100 people were at the concert, but only a handful remained at the venue when the shooting happened, officials said.
Mr Mina said unarmed security guards checked bags as people entered the venue but no metal detectors were used and no body searches were made.
News of the attack spread quickly on social media, with many fans voicing their shock and anger.
When the first reports of the shooting surfaced, #PrayForChristina was the top trending hashtag on Twitter.
It changed to #RIPChristina after the death was confirmed.
Ms Grimmie first came to prominence as a teenager for her renditions of hit songs, amassing a huge following on YouTube.
In 2011, she released her debut musical recording Find Me. Her second EP – Side A – followed in February 2016.