Manchester City, the third English side in through to the knockout stages, will play Dynamo Kiev in a tie for which the game in Ukraine must be played behind closed doors.
The first legs of the ties, which were drawn at UEFA headquarters in Nyon, will take place on February 16/17 or 23/23 with the return matches on March 8/9 or 15/16.
The Gunners, who reached the last 16 with a memorable victory at Olympiacos in their final group game, knew they could have faced Barca or 10-times winners Real Madrid.
Their task will be a daunting one and Barca, having beaten Manchester City at this stage for the last two seasons, will be clear favourites.
Chelsea face PSG in the knockout stages for the third season in succession and will hope to gain some revenge after losing to them in March.
City will be pleased to have avoided the dangerous PSG as they bid to reach the quarter-finals for the first time but their fans may be frustrated about the Kiev situation.
The Ukrainian club were ordered to play two games behind closed doors last month as punishment for offences that included racial abuse of players by supporters during their group game against Chelsea.
City fans already boo the Champions League anthem in protest against UEFA, chiefly because their fans were not allowed to travel to a game at CSKA Moscow last season. That situation was slightly different, however, as some fans had already made visa, travel and accommodation arrangements before the ruling was made.
Bayern Munich were handed a tough-looking draw against Juventus, runners-up last season, while Real Madrid will also face Italian opposition in Roma.
Wolfsburg and PSV Eindhoven, the two sides that qualified at Manchester United’s expense, were paired with Gent and Atletico Madrid respectively.
The other tie in the round sees two-time winners Benfica come up against Zenit St Petersburg.
Draw in full:
Dynamo Kiev vs Manchester City
Benfica vs Zenit
PSV Eindhoven v Atletico Madrid
Juventus vs Bayern Munich
Arsenal vs Barcelona
PSG vs Chelsea
Roma vs Real Madrid
Gent vs Wolfsburg