The singer - who was a member of Joel Madden's team - appears on Guy Sebastian's new single 'Gold', also appearing in the video. She was asked to leave the programme when producers deemed that she had an unfair advantage over other contestants ahead of the forthcoming live shows.
"It saddens me that I am leaving The Voice earlier - much earlier - than I had hoped," Smith said in a statement. "However, I've loved every minute of it and respect the decision that has been made by Joel and his team.
"I've sung on Guy's albums and been part of his band for many years so I'm thrilled to be in the clip and am looking forward to getting back to work and also working on my solo career."
"Our priority as we move into the voting period toward the finale is that all of the artists are on a level playing field," Nine Network director of development Adrian Swift added.
"In our business we are often confronted by these tough decisions and unfortunately at this time it's been decided that it isn't appropriate for her to remain in our competition. We wish Carmen well and thank her for a wonderful contribution to the show thus far."
Sebastian also expressed his disappointment during an interview on Fox FM, saying: "She's the most honest, thoughtful, real sweet girl. She's a very close mate and so yes, everyone's a bit devo'd.
"It's one of those things, we just don't get it."
Watch the video to 'Gold' by Guy Sebastian below: