David Moyes' men have made a slow start to the season and a loss at Old Trafford to the English Premier League leaders would be a huge blow to their title chances.
Vidic said his men needed to step up for the visit of Arsene Wenger's side and wants them to take their chance to prove themselves.
"We have to step up for a big game like this. We have to prove to everyone, including our fans and ourselves, that we are good. That is the challenge for us," the Serbian defender said.
"Arsenal have played really well this season but we have to show we can do better than we did in games like Manchester City (in a 4-1 loss in September).
"I have seen signs we are getting better but good players raise their performances in big games and Arsenal is definitely a big game and one we're looking forward to."
United are unbeaten in their past four matches against Arsenal, including an 8-2 thrashing in August 2011.
But Vidic warned his team-mates that this season's Arsenal side are a much more dangerous outfit with midfielders Mesut Ozil and Aaron Ramsey in top form.
"This is different to recent years. We are looking at them more seriously. Arsenal are playing well, top of the league," he said.
"They are in the best form of all the teams competing for the title and I think we need a performance at home.
"We need to pay attention to details and defend right, create chances and score goals.
"A lot of things are getting better and better, but we need them to be even better against Arsenal. They present challenges for defenders."
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