Rangnick was appointed yesterday but he is yet to receive his work permit and caretaker boss Michael Carrick will be in the dugout when the Gunners travel to Old Trafford.
United said in a statement: “While the club follows the regulatory process around a work visa, Carrick will continue at the helm.”
Rangnick is now expected to officially take charge of United for the first time against Crystal Palace on Sunday.
The situation is not ideal for United, who were eager to make a swift appointment following the sacking of Ole Gunnar Solskjaer in a bid to avoid their season being further disrupted.
Carrick has operated as caretaker while Rangnick’s contract was finalised – securing a win against Villarreal and a draw at Premier League leaders Chelsea on Sunday.
Rangnick has signed a six-month deal and a further two-year consultancy role.
Carrick and rest of Solskjaer’s key backroom team will continue at the club, despite Rangnick planning on bringing in some of his own staff.
Rangnick said: “I am excited to be joining Manchester United and focused on making this a successful season for the club. The squad is full of talent and has a great balance of youth and experience.
“All my efforts for the next six months will be on helping these players fulfil their potential, both individually and, most importantly, as a team. Beyond that I look forward to supporting the club’s longer-term goals on a consultancy basis.”