The European champions spluttered to a 1-0 win over Stoke on Saturday to ensure they ended the weekend a point clear of Manchester United at the summit.
Chelsea have enjoyed a near-perfect start to the title race in terms of results, winning four of their five games and keeping four clean sheets.
But they have yet to face any of the current top nine in the league.
Full-back Ivanovic insisted it was far too early for Chelsea to be thinking about regaining the title they last won in 2010.
"We have the next game as a very great challenge for us in the Premier League - Arsenal away," he said. "This is the first actual big game for us this season."
The 28-year-old added: "Our performances and quality - we know how it is.
"But we have to show everyone, and we have to show it every game.
"This is the biggest challenge. I think Arsenal will be a great challenge for us, and we have to really be ready for that."
Chelsea will need to play much better than they did on Saturday to get anything from the Emirates Stadium.
Their £130million attack huffed and puffed and it needed Ashley Cole's first goal in 28 months to snatch all three points.
Ivanovic, who could not have a more different scoring record from full-back, was full of praise for the man who plays on the opposite flank.
"For me, Ash is the best left-back in the world - for a long time," Ivanovic said.
"He is really great, and always makes a lot of good things for the team.
"We're really happy for him because, for defenders, it is always nice to score goals for the confidence. Ashley is really fantastic.
"He has the skill, he has the speed, he can run, he can go up front, he has the vision of the game, he defends well, he is quick. But I think all this is nothing new!"
With Saturday's game being a potential turning point in the title race, Cole and Ivanovic could both find themselves rested for Tuesday night's Capital One Cup clash with Wolves.
Manager Roberto Di Matteo has already confirmed he plans to field a mix of regulars, fringe men and youth-team players.