The Gunners will host the reigning champions at the Emirates Stadium between January 9 and 13 in one of 32 matches.
They meet in the Premier League on Wednesday night but return to north London just weeks later for another massive clash.
Record 14-time winners Arsenal last lifted the FA Cup in 2020 but have not progressed past the fourth round since.
The third round has seen all Premier League and Championship teams enter the competition, with a variety of ties being drawn.
Meanwhile National League side Tamworth, the lowest-ranked team left in the FA Cup, will play Tottenham at The Lamb Ground in what is a huge tie for the club.
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They have already beaten two League One sides en route to the third round, though Spurs will present a whole different challenge.
Elsewhere, Liverpool face Accrington Stanley at Anfield, Chelsea host Morecambe and Manchester City are at home to Salford City.
As for fifth-tier outfit Dagenham & Redbridge, they will face Millwall at The Den, with Bromley of League Two travelling to Newcastle.
Just one all-Premier League tie has been drawn in the third round this season as Aston Villa take on West Ham.
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Leeds United will come up against Harrogate Town in a Yorkshire derby at Elland Road.
Frank Lampard's Coventry City have been drawn at home to Sheffield Wednesday, with Wayne Rooney and Plymouth Argyle set to travel to Brentford.
This is the first season without replays in the competition, with first and second round matches being decided by extra-time and, if needed, penalties.
Three of the weekend's matches were decided by spot-kicks including Tamworth, who beat Burton Albion on Sunday.