The 19-year-old told followers on her Twitter account that she was "crying" after Carey responded to a series of messages that Amaro had sent her via Twitter following this week's Top 5 performances.
Amaro had told Carey: "I would like to just say I absolutely love you and your music has helped me through a lot of hard times. Thank you so much for being the music angel you are and blessing this earth with your angelic voice.
"You truly are one of the reasons I sing. YOU are one of my biggest inspirations thank you from my heart. Hope to hear back :-) (sic)"
Carey later responded on her own Twitter feed: "Dear Melanie, you should be very proud of yourself and the beautiful gift you've been given. Thank you so much for your incredibly kind and humbling words. Never give up, never let go, no matter what. xo, MC."
Amaro then wrote: "Omg God is good!!! Mariah Carey just tweeted me. I'm literally crying, she is my role model and one of the people who inspires me to sing :-)."
Amaro, who is being mentored by Simon Cowell, performed the Mariah Carey and Whitney Houston track 'When You Believe' for her contestant's choice song on last week's X Factor live performance show.
She said: "I chose this song because it's a song that describes my journey and everything I've gone through with going home and coming back, I had to continue believing."
Judge Nicole Scherzinger said: "You gave me goosebumps all over and what was so special about that performance is you didn't just sing the song, I felt like you were speaking the song to each and every one of us and believed every single word you were saying."
Amaro also performed a dance remix of 'Someone Like You' by Adele, with both performances earning her enough public votes to advance to the semi-final.
Rachel Crow was sent home on last week's live results show, leaving Amaro to battle Josh Krajcik, Marcus Canty and Chris Rene in the race for the $5 million recording contract prize.
X Factor continues Wednesdays and Thursdays at 8/7c on Fox
> X Factor Rachel Crow: 'Exit was God's plan'
> Read Digital Spy's full X Factor headlines
Watch Melanie Amaro perform 'When You Believe' below:
Browse a gallery of pictures from the results show below: