An unfortunate own goal from Christian Fuchs and a late second from Eddie Nketiah was enough to send the Gunners through. The Foxes made 11 changes to their team after beating Burnley at the weekend and they struggled to find their feet against Mikel Arteta's side.
Arsenal will now progress into the fourth round and will now face Liverpool or Lincoln City away from home.
Story of the match
Both teams began the game brightly and created chances in the opening five minutes.
Reiss Nelson curled a right-footed shot towards the top corner but Leicester goalkeeper Danny Ward managed to use his fingertips to prevent an early goal. Kelechi Iheanacho was then found brilliantly by Marc Albrighton at the other end of the pitch, but the Nigerian's effort was saved easily by the onrushing Bernd Leno.
After a short period of shared possession, Arsenal began to push for the opener. Bukayo Saka whipped a dangerous low cross into the box but neither Eddie Nketiah nor Joe Willock could get a touch on the ball.
Saka was once again heavily involved in the action four minutes later as he broke into the Foxes box. The England U-21 international tangled legs with Daniel Amartey in the area but penalty appeals were waved away by the referee.
There was no VAR in use at the King Power Stadium which helped to spare the blushes of Amartey, who was starting his first game in 23 months since his horrific leg break two seasons ago.
In the final 15 minutes of the first half, both teams had their best chances. An unmarked Nelson somehow missed the target from 10 yards out and James Maddison had a superb curling effort rebound back off the post and into Leno's hands.
The second half started slowly with extremely wayward long-shots from Maddison and Demarai Gray the only highlights.
Arsenal then stepped their performance up a gear and gained the lead just before the hour mark. After some scrappy play in the area, Nicolas Pepe attempted a pass across the box which deflected onto the post and then into the legs of Fuchs who couldn't do anything to prevent the ball heading into the back of the net.
Once they had gone a goal down, Leicester failed to get a foot back into the game and struggled to string any attacking moves together to get past a tough Gunners defence.
Nketiah then sealed the victory for Arsenal as he stumbled into the six-yard box and poked the ball past Ward.
Carabao Cup was not the priority for the Foxes this season
Brendan Rodgers made 11 changes to his Leicester side after their 4-2 win over Burnley at the weekend, giving the indication that the Foxes were not too interested in going on a cup run this season.
With European football now on the calendar, the fixture list was already going to be busy, so the Carabao Cup was only going to add more games.
Despite having a brilliant cup run last year, it does seem as if the Premier League and Europa League will be taking priority this season, and maybe falling at the first hurdle will benefit the Foxes in the long run.