The five-time Wales international arrived to try and keep his new side in the Football Leagu.
However, he missed a 1-0 defeat to Bradford City due to unfortunate circumstances away from the pitch.
Explaining the absence post-match, Carlisle manager Mike Williamson said: "He's okay. He had a car accident, so he spent the day just getting a few tests done.
"But no, he's healthy, so he should be back in training Monday and he'll be fit for next weekend."
The 33-year-old Dummett brings a wealth of experience to Carlisle.
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He recorded 151 Premier League appearances alongside three goals.
Dummett made all of those appearances exclusively for Newcastle, his local side, with some alongside his new manager Mike Williamson.
He departed the club last summer as he looked continue his career in the Football League.
Wigan Athletic in League One were his first destination, but he only made five appearances before dropping down a level to his new side.
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Carlisle need all the help they can get too, as they're currently rock bottom of England's top four professional tiers.
Sitting 24th in League Two, they're on 18 points from 24 games, seven from Tranmere and safety.
The Cumbrians have been in the top four tiers since 2006, and even spent the 2023/24 season in League One.
And now, with relegation to the National League looking likely, the club are going all-out in the transfer window.
Dummett is one of nine winter arrivals and by far the most experienced, but Manchester United loanee Joe Hugill has caused some excitement as a goal-scoring striker.
Commenting on the 21-year-old, manager Williamson said: "Joe put in a real shift and you could see he's threatening.
"He's going to get goals when he gets chances. So, we need to create more clear-cut chances."