The hitmaker revealed she grew close to Dolly, 73, during her guest appearances on Disney Channel show "Hannah Montana".
"She doesn't really let me call her a godmother. She likes fairy godmother much better," Miley told Entertainment Tonight, and said the country singer "deserves the honour because of her kindness."
The newlywed singer performed a rendition of Dolly's 1983 duet with Kenny Rogers, "Islands in the Stream", with Shawn Mendes and Mark Ronson. Miley then teased the possibility of another collaboration with Shawn at the upcoming Grammys on Sunday, February 10.
Pink was also one of the performers at the event, and kicked off the celebration with a show-stopping performance of Dolly's song, "Jolene". Willie Nelson teamed up with Brandi Carlile for "Everything's Beautiful (In Its Own Way)", while Katy Perry and Kacey Musgraves delivered a sassy rendition of "Here You Come Again".
"Dolly is someone that just continues to give, whether it's giving us music, giving us inspiration," 26-year-old Miley added. "She's taught us all so much and we were just saying, it's about time that this happened."
Dolly later joked onstage in a speech that she was a hillbilly, and even called out Miley's father, Billy Ray Cyrus.
"Now, I want to thank all of you for this wonderful night," she said. "I truly am honoured to be MusiCares person of the year, and the first country artist to be honoured. Of course you know us hillbillies, we need things too. We may not have had the sex, drugs and rock n' roll, but two out of three ain't bad tonight. Right, Billy Ray Cyrus?"
The country singer performed her 1971 song, "Coat of Many Colours", with friend and musician Linda Perry.
Dolly later laughed, "I just hope I live long enough to get the Betty White longevity award."