The stalemate means Atletico move up to second in the table but could be overtaken by both Barcelona and Sevilla on Thursday. Barca play away at Real Sociedad after Sevilla travel to Levante.
Real Betis, who were beaten by Elche on Tuesday, are four points behind Atletico in fifth.
After six consecutive victories between February and April, Atletico have now managed just one win from their last five in all competitions, bringing back some of the concerns that hung over the team earlier in the season.
Without Joao Felix, who will miss the rest of the season through injury, La Liga’s reigning champions lacked the thrust needed to break down a determined Granada side, who were playing their first match under new coach Aitor Karanka.
Granada sit 18th, a point behind Cadiz, who have a game in hand.