The London club, which won at Olympiakos in the final game of the group stages to ensure qualification
, was handed the toughest possible assignment against the titleholder in Monday's draw at UEFA headquarters in Nyon, Switzerland.
In-form Barcelona sits top of the Spanish league despite drawing its last two matches, and Arsenal manager Arsene Wenger has to work out how to achieve the seemingly impossible -- keeping attackers Lionel Messi, Luis Suarez and Neymar quiet.
Arsenal secretary David Miles told BT Sport Barca was "the team most Arsenal fans would have wanted to avoid."
He said: "On the back of the great win [against Olympiakos] in Athens, we were hoping for a good draw today. I think it's the tie of the round.
"It's not going to be easy -- it's the team that most Arsenal fans would have wanted to avoid at this stage -- but it's up to us to make a good fist of it."
Barcelona director of sporting institutional relations Albert Soler said he was looking forward to "a very attractive game."
"English teams are always very strong," he told Eurosport. "We need to play to the best of our abilities. Arsenal are not favorites here, but we don't consider ourselves outright favorites.
"Arsenal are a strong team and we'll have two great teams playing two great games."
Arsenal and Barca have met three times in the competition over the last decade.
In the 2006 final, the Catalan club won 2-1 thanks to a late Juliano Belletti goal, and in 2010 Arsenal lost 6-3 on aggregate in the quarterfinals.
The most recent meeting came in 2011, when Arsenal won the home leg 2-1 but ended up losing the last-16 clash 4-3 on aggregate.
In other high-profile ties, struggling Premier League winner Chelsea takes on French champion Paris Saint-Germain and last year's runner-up Juventus plays German champion Bayern Munich.
Real Madrid faces Roma, Manchester City takes on Dynamo Kiev while Belgian club Gent plays Wolfsburg, the club that eliminated Manchester United.
Dutch team PSV Eindhoven plays 2014 finalist Atletico Madrid, and Benfica tackles Zenit St. Petersburg.
PSG is reunited with Chelsea after beating the London side in last season's competition, winning on away goals in the last 16 after a dramatic 2-2 draw at Stamford Bridge followed a 1-1 stalemate in the French capital.
On its Twitter feed, Chelsea posted: "We meet again ... see you again soon, PSG."
The London club's general secretary David Barnard said: "There is not much we don't know about Paris," while PSG sports director Olivier Letang told reporters: "You only know if it's a good draw after the tie. We are ambitious."
Bayern Munich defender Philipp Lahm said the draw against Juventus had set up "a European classic" and added: "Juventus made the final last season, so it is a big challenge -- but we want to reach the quarterfinals and will give everything to do so.
Juve legend Pavel Nedved said he was "confident, even though we know Bayern represent very tough opposition."
Meanwhile, Manchester City fans will be unable to travel to Kiev after the Ukrainian club was ordered to play its next European game behind closed doors due to crowd racism and disturbances during October's group game against Chelsea.
City director of football Txiki Begiristain said Kiev "will be difficult for us." "They are growing in the competition and it will be a big challenge, but we hope to be ready," he told reporters.
Kiev coach Sergei Rebrov said City is "a solid and well-balanced team" but added: "We have already played against them and enjoyed success. Everyone has weak points, and our job is to find them."
Real Madrid director Emilio Butragueno said the club's players would need to be on their guard against Roma, adding: "If we see ourselves as favorites, things won't go well for us. We know what can happen if you have even 10 poor minutes on a European night."
Roma coach Rudi Garcia said: "Real Madrid will be favorites. We faced Barcelona in the group stage, and now it is Real Madrid, but we are in the Champions League for this reason. All the players are ready and are looking forward to this game."
The matches take place over two legs with the group-winning teams away from home first. The first-leg games will be played on February 16 and 17, with the returns taking place on February 23 and 24.
The draw system means no team can play any club from its own domestic competition or from its Champions League qualifying groups -- so a possible Clasico clash between Barcelona and Real Madrid or an all-English tie could not happen until the quarterfinals.