Mills, who was among the favourites to win the series, crashed in training and injured her knee and thumb.
Sir Paul McCartney's ex-wife was only called up as a replacement this year, having had to pull out of a previous series of the Channel 4 show due to injury.
Mills is the second celebrity to leave the Austria-based show this week, following former Girls Aloud singer Sarah Harding out of the competition after she ruptured a ligament.
The show's third series has been plagued by injuries.
Britain's most successful gymnast, Beth Tweddle, 30, needed neck surgery following a fall during training.
Former Olympic champion swimmer Rebecca Adlington, Holby City actress Tina Hobley, Made In Chelsea's Mark-Francis Vandelli and Olympic gold-winning medallist Linford Christie have already departed the contest.
Mills and Harding have been replaced by former England rugby player Ben Cohen, and ex-EastEnders actor Joe Swash, a serial reality television contestant.
Cohen said: "Being a skier myself it was a no-brainer for me to join the cast of The Jump. I've always really enjoyed watching the show and I'm really pleased to be a part of it. I'm looking forward to competing and hope to make it to the final. I'm here to make the most of the experience."
Swash said: "I'm so excited to be a part of The Jump. It is an opportunity that I couldn't refuse and I am delighted to be experiencing this for myself. I cannot wait to get going."
Singer Brian McFadden was eliminated on Sunday's show for a poor performance on the parallel slalom.
The final will be held next Sunday.