Click on the video below to hear Katy's message.
When Olivia Wise posted a YouTube clip of herself covering Katy's latest hit Roar, the video went viral and gained nearly 190,000 hits within two weeks.
Katy was clearly touched by Olivia's rendition, and sent the teenager a video message back.
"Hey Olivia, it's Katy Perry here," the pop star says in her clip. "I just wanted to reach back out to you and tell you that I saw your video and was very moved.
"You sounded great, and for being in the studio and making your wish to record that song — I thought that was really cool.
"I love you and a lot of people love you, and that's why your video got to me and it moved everybody that saw it.
"I just wanted to send you some love and some light and tell you that I'm thinking about you. Thank you so much. Keep roaring."
The Firework singer also included a link to a fund in Olivia's name to raise money for brain tumour research.
Scroll down to watch Olivia's cover of Roar.
While Olivia's condition has deteriorated in the past few weeks, the video message from Katy gave the teenager "an important boost" and "meant the world" to her, according to Olivia's cousin Jeff Kasel.
It was Jeff who arranged for Olivia to get some recording time in the studio, and even though she was "managing a lot of pain" at the time, Olivia sang Katy's anthem to self-confidence beautifully.
"I am a champion and you're going to hear me roar," sings Olivia, sitting in a wheelchair as a smile breaks across her face.
"You hear the song totally different," said Jeff. "It gave the song a stronger meaning. I didn't see it before. To me it was a fluffy song that doesn't sound so fluffy when she sings it."