Messi had scored 37 in his 38 previous outings against Sevilla, more than against any other team, but a series of threatening free-kicks were repelled by the home side this time.
Antoine Griezmann was surprisingly left out of Barcelona's starting line-up for the clash with third-placed opposition, as Martin Braithwaite was preferred, and the visitors lacked penetration.
The draw leaves them still top of the table, but Real Madrid, with a game in hand, is just three points off the summit.
This stalemate at the Ramon Sanchez Pizjuan stadium could prove a costly one for Barcelona come the end of the season, and it was almost worse for them, with Sevilla's Sergio Reguilon, on loan from Real Madrid, squandering a glorious late chance.
Sevilla defender Jules Kounde drilled an early shot a yard wide, but Barcelona was soon on top and for a while looked terrific.
It took two Sevilla players to stop Messi at the expense of a free-kick on the edge of the penalty area at the 20-minute mark.
Up stepped Messi, and his shot beat the wall and might have beaten Tomas Vaclik too, but the goalkeeper was done a favour by Kounde, who cleared the ball from almost on the line with a flicked header over the bar.
Messi tested Vaclik moments later with another free-kick, and the goalkeeper was more comfortable second time around.
Inevitably at the centre of things, Messi avoided punishment for shoving Diego Carlos to the ground in first-half stoppage-time after the home defender fouled Suarez.
Marc-Andre ter Stegen came to Barcelona's rescue early in the second half with a fine parry to deny Lucas Ocampos, the goalkeeper's strong left hand keeping out a thunderous shot from a tight angle to the right of goal.
The German thwarted Munir moments later too, pushing away a vicious left-footed strike.
Vaclik tipped another Messi free-kick over his crossbar at full stretch as the game entered its final 20 minutes, before Jordi Alba made a key block at the other end as Sevilla launched a three-on-one breakaway raid.
Ocampos drew a save from Ter Stegen with a low shot but neither side could successfully plot a way to a goal, Reguilon failing to properly get hold of a close-range shot at the death, to Barcelona's great relief.