A stunned looking Anderson said afterwards she was sad to have been knocked out, but added: "I just stumbled, my dress... my boobs fell out, it happens."
Despite sitting third following the judge's vote, Anderson and partner Matt Evers took part in the "safety skate" against Chegwin and Olga Sharutenko after slipping into the bottom two once the public votes were added.
The judges unanimously voted to axe the Canadian-born actress.
Writing on Twitter afterwards, Anderson added: "Thanks for everything. Sorry I was voted off. My dress fell apart in save-me skate. Devastated."
When she came off the ice, presenter Phillip Schofield quipped: "If it had happened a little earlier this evening you'd have been guaranteed a place in the final."