Rangnick was handed the Manchester United reins on Monday on a deal that will run until the end of the 2021/2022 season when a new manager is appointed.
But the 63-year-old German is still working to acquire his work visa, which will make him unavailable to sit on the bench against the Gunners at Old Trafford.
Carrick has overseen Manchester United’s last two games since Ole Gunnar Solskjaer was sacked, winning 2-0 against Villarreal in the UEFA Champions League and getting a creditable 1-1 draw against leaders Chelsea in the Premier League on Sunday.
The 40-year-old will once again direct affairs from the touchline when Arsenal come visiting.
In a statement on their official website, United said: "Ralf Rangnick was announced as interim manager on Monday but, while the club follows the regulatory process around a work visa, Carrick will continue at the helm.
"Michael has communicated this to players and staff at Carrington in a busy week for the club."
Ragnick will hope to get his permit on time for this weekend’s home game against Crystal Palace.
The Red Devils lie eighth on the table and will hope to secure maximum points in their next two matches.
