The Brazil international will miss the clash at the Emirates after picking up his fifth yellow card in the league this season during the 1-1 draw at Crystal Palace in midweek.
"We have an idea of how to deal with that," Ten Hag said of playing without Casemiro, who only came off the bench for the last 10 minutes in September's game at Old Trafford which United won 3-1 to hand Arsenal their only league defeat this season.
United are on a 10-game unbeaten streak in all competitions and sit third in the league on 39 points after 19 games, eight points behind Arsenal who have a game in hand.
Ten Hag said Mikel Arteta's high-flying team have a "really good structure".
"It is a really good mentality and a winning attitude in the team. That is why they are top of the list," he said. "They are in a great run. It is up to us to beat their run and we will do everything to do that."
United's new signing Wout Weghorst (30) started as their sole striker in the Palace game, days after joining the club until the end of the season on a loan deal from Burnley.
Asked if United would sign more players in the January transfer window, Ten Hag said: "I think as Manchester United you always have to look for solutions, and always you have to look for better and that is what we will do.
"We will be doing our research and if there are opportunities, we have to go for it."
Winger Jadon Sancho (22) returned to team training this week for the first time since October but Ten Hag did not mention if he would feature in Sunday's game. The Dutchman said last month that Sancho was "not in the right status or fitness state".
Ten Hag also did not provide updates on the fitness of injured duo Diogo Dalot (23) and Anthony Martial (27).
