The 20-year-old's time at Highbury was due to expire after Saturday's 2-0 loss to Cheltenham but both parties have agreed to continue the deal until the end of January.
Carr has made three appearances for the Cod Army, starting for the first time in the weekend's defeat.
"It's good that Fleetwood have been impressed by him and want to keep him at their club for the busy festive period, but the next challenge for Daniel now is to force his way into Graham Alexander's starting XI.
"It is important for Daniel's development that he gets more experience of senior football in a team near the top of a tough division."
- Sports & Recreation