The Magpies will take on the Spanish giants over two legs in the last 16, with a quarter-final clash against Tottenham or Atletico Madrid at stake.
The first leg against Barcelona will take place at St James' Park on Tuesday, March 11 or Wednesday, March 12. The second leg tie will then be held the following week, again either on the Tuesday or the Wednesday.
The winners will then take on Spurs or Atletico, and whoever comes through that game will take on Arsenal, Bayer Leverkusen, Sporting or Bodo/Glimt in the semi-finals.
Howe described reaching the last 16 of the competition as "really special and really, really positive".
The Magpies have already played Barcelona in the league phase in this season's competition, going down 2-1 at St James' Park.
Speaking before the draw took place, Howe said on Friday morning: "We deserved more from the game, we played very well.
"We're in a great position where whoever we get, it's sort of mouth-watering for us and a great thing to look forward to."
Elsewhere in the draw, Manchester City will take on record winners Real Madrid, while Liverpool were drawn against Galatasaray. Chelsea will face holders Paris St Germain.