Diego Simeone's side was held at home to Malaga on Sunday, while the Catalans were unable to beat Elche, meaning the title will now be decided at Camp Nou next weekend.
A goalless draw at Elche for the Blaugrana meant Atletico would have won the title with a victory at home to Malaga, but Diego Simeone's side was held to a 1-1 tie at home to Malaga.
The two teams therefore both remain in control of their own destiny ahead of a mouth-watering decider in the Catalan capital next Sunday.
Atletico, unbeaten in five fixtures against Barca in 2013-14, now needs only a point at Camp Nou in the last round of La Liga to be crowned champion, while the Catalans must beat Simeone's side to claim the title via their head-to-head record.
A win for Gerardo Martino's men would see both teams finish the season on 89 points, but Barca would prevail thanks to superior head-to-head record in the two meetings between the sides (the first was a 0-0 draw and Barca would have won the second).
Real Madrid, meanwhile, is out of the race altogether after losing 2-0 at Celta Vigo on Sunday, but Carlo Ancelotti's side will finish second if it beats Espanyol next weekend and Atleti defeats Barca at Camp Nou.