The Glasgow giants, who finished second in last season's Scottish Premier League, will play away in the first leg of the tie on July 27 or 28 with the return at Parkhead on August 3 or 4.
Victory would take Celtic through to join the likes of Tottenham, Sampdoria and Sevilla in the play-offs for a place in the group stages, which begin in September.
That play-off round is due to take place on August 17-18 and 24-25.
Braga, who play at the distinctive AXA Stadium, a venue carved out of the rock face of a former quarry, finished second to Benfica in their domestic competition.
It is their first foray into the Champions League.
Celtic reached the play-off round last season only to lose to Arsenal.
Defeat in the tie would leave Neil Lennon's side in the play-off round of the Europa League along with clubs such as Dundee United, Manchester City and Aston Villa.
The first leg will be Celtic's first competitive match of the new season, with their Scottish Premier League campaign not beginning until their trip to Inverness on August 14.
Elsewhere in the draw, the winners of the second qualifying round clash between Bohemians and The New Saints were paired with Anderlecht.
Irish champions Bohemians lead their Welsh counterparts 1-0 after the first leg earlier this week.
Dutch giants and four-time winners Ajax will play Greek club PAOK and Ukraine's Dynamo Kiev face Gent of Belgium.
Zenit St Petersburg, who beat Rangers in the 2008 UEFA Cup final, face Romanians Unirea Urziceni.