The 36-year-old actor, who stars in the musical alongside stars like Tom Cruise and Catherine Zeta-Jones, described Baldwin's mouth as a "cave of wonder".
"The inside of [Alec's] mouth is beautiful it's like a cave of wonder. It's like going into a cave where civilization began and up on the wall there's ancient etchings, code, the very DNA of our species written on his gums.
"His teeth are like living monuments to God," said Brand. While Brand, who split from wife Katy Perry in December, may have enjoyed kissing Baldwin, he said he doesn't believe the pair could ever be a couple.
"I think if I was in a relationship with Alec Baldwin, he'd be the one who would want to be in charge and that would annoy me," Brand joked. "Rock of Ages", which also stars Julianne Hough, Mary J Blige and Diego Boneta, hits theaters on June 15.