The star, who was performing in New York, collapsed to her knees when the projectile struck the side of her head.
She was later escorted from the venue, apparently still in pain, with her hands pressed to her face.
Video posted online showed a man being removed from the crowd by security as fans shouted "that's assault".
New York Police later confirmed that a 27-year-old concertgoer had been charged with assault.
Video on social media shows a phone being thrown from the audience during a concert at venue Pier 17 in New York City and hitting Rexha mid-performance in the face.
New York City Police Department told multiple news organizations that Malvagna was arrested and charged for the incident.
The singer, whose hits include I'm Good (Blue) and Meant To Be, posted photos showing her injuries to Instagram on Monday.
They showed bruising around her left eye and a cut on her eyebrow. However, she captioned the pictures, "I'm good", and gave the camera a thumbs-up.
Gossip website Pop Base quoted her mother as saying the star received medical treatment and needed three stitches.
BBC has contacted Rexha's team for further comment.
It was the last song during her set at The Rooftop at Pier 17 Sunday night when the pop performer asked the crowd to put their phones away to enjoy the experience without distractions.
"She literally said, 'thank you so much for all of your support you are the best,' then boom," concertgoer Ross Bernard said.
The crowd was stunned as they watched the singer drop to the ground.
"I thought it was a CD case, saw her drop down, security grabbed it, it was a phone," Ron Bosch said.
Sunday night's concert was part of Rexha's "Best F'n Night of My Life Tour." Her next concert is scheduled for Tuesday in Philadelphia.
Nicolas Malvagna, 27, of New Jersey man was released without bail after being arraigned Monday on assault, aggravated harassment and other charges. Each is either a misdemeanor or a violation.
According to a court complaint, Malvagna told a third party he tried to hit Rexha with the phone at the end of the show because he thought "it would be funny.”
A message seeking comment was sent to his attorney.
A three-time Grammy nominee, Rexha is known for such hits as “I’m Good (Blue),” “Meant to Be,” featuring country’s Florida Georgia Line, and “I Got You.” Raised in New York, she was a songwriter for other artists before becoming a solo star.
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