The Blaugrana's 100 per cent record in La Liga came to an end after a battling display from the hosts at La Rosaleda
Luis Enrique's men came into the fixture at La Rosaleda having won all four of their opening league fixtures without conceding a single goal.
And, while the Catalan outfit were able to preserve that impressive defensive record, a failure to turn possession into goals will disappoint their coach.
Jordi Alba proved to be a constant menace down the left in the first half, but the visitors were unable to make the most of his repeated dangerous deliveries.
Claudio Bravo pushed a Luis Alberto free kick onto the post midway through the second half, and Barca held on for what eventually turned out to be a hard-fought point.
The result sees Barcelona, who had won the last 12 league meetings between the sides, remain top on goal difference from Sevilla, while Malaga maintain their record of having not conceded at home this season.
Luis Enrique continued to rotate his defence by bringing Gerard Pique, Marc Bartra and debutant Douglas in for Javier Mascherano, Jeremy Mathieu and Dani Alves following the 5-0 demolition of Levante on Sunday, while Neymar was fit to start after recovering from an ankle injury.
Barca applied the early pressure and Malaga defender Sergio Sanchez did well to thwart threatening crosses from Pedro and Ivan Rakitic, but Bravo had to be alert at the other end to get his body behind a drilled effort from Nordin Amrabat.
The half continued at a frantic pace and Messi - chasing his 400th senior goal for club and country - curled a free kick from 20 yards over the crossbar, before Pedro diverted just wide from an Alba cross.
Having seen close-season signing Luis Suarez score twice for Barcelona B in a friendly against an Indonesia XI earlier in the day, the visitors' starting attackers might have been feeling the pressure to perform ahead of the Uruguayan's October return from suspension, and Messi should arguably have done better when he chested wide from another Alba ball into the area.
Barca were dominating possession, but a failure to truly challenge Malaga goalkeeper Carlos Kameni saw them enter the break without finding the net, despite Alba's effervescent running down the left wing.
Luis Enrique wore a stern expression on the touchline as Malaga continued to frustrate their visitors at the start of the second half.
Bartra headed narrowly wide from a corner on the hour mark, before Neymar's match came to an end when he was replaced by Munir El Haddadi on 64 minutes.
Roberto Rosales' drilled effort shortly afterwards drifted wide, but served as a reminder of Malaga's attacking threat, and Luis Alberto's free kick – palmed onto the post by Bravo – reaffirmed that point.
Malaga captain Weligton was perhaps lucky not to escape harsher punishment as he was shown a yellow card for grabbing Messi's face in a late scuffle.
But 0-0 is how it would remain, as Luis Enrique suffered his first minor setback since taking the reins at Camp Nou.