The result means it's still all to play for in Dortmund in next Tuesday's second leg, although the Bundesliga side may live to regret not grabbing an away goal.
Borussia do however remain the only unbeaten team in the Champions League this season, while Malaga extended their unbeaten home record in Europe to 14 games.
Afterwards Malaga winger Joaquin Sanchez said the tie is still wide open.
"It's a positive result for us, if we score in Germany it complicates things for them, so I think we go there with the same chances as they have," he told Spanish television.
His coach Manuel Pellegrini, who is attempting to become the first coach to take two teams to the Champions League semi-finals in their debut season in the competition, agreed.
"I don't think the game in Germany will be too different from tonight, only an early goal for either team could change things. Both sides went for it tonight and it made for a good open game," he said.
Dortmund coach Juergen Klopp was also satisfied with the draw.
"I can live with this 0-0. We did everything well from the first kick to the final whistle but it's a higher level," he said.
"We know what we have to do in the return match."
Both sides were understandably cautious in the opening stages but Javier Saviola came close to opening the scoring for the home side on seven minutes after good play on the right from Jesus Gamez found the Argentinian in space in the box.
Shortly after, the German side had their first of many first-half chances when a long ball out of defence was headed into the path of Mario Goetze by Robert Lewandowski, but Willy Caballero was quick to get down and save for the hosts.
Caballero was the hero again five minutes later when he made an even better save at close range from the same player after slick passing from the Germans had opened up the home defence.
Goetze felt he'd let his side down by missing those chances.
"I could have really helped the team by scoring. I'm ashamed that I didn't score at least one of them," he said.
Borussia's neat quick passing game was beginning to dominate proceedings and Caballero had to be sharp again on 25 minutes to deny a Marco Reus drive from outside the area.
Next it was Kevin Grosskreutz who shot wide for the visitors after another quick move caused more problems in the Spanish defence.
On the half-hour mark, Malaga centre half Weligton received a yellow card when all he could do was pull down Lewandowski to stop another attack, with the booking meaning the influential Brazilian defender will miss the second leg in Germany.
Malaga midfielder Manuel Iturra will also miss the second leg after picking up a card later in the game.
Borussia's Polish forward Lewandowski was looking lively and causing Malaga problems at every opportunity but, at the other end, the hosts showed signs of causing their own problems and Roman Weidenfeller needed quick reflexes to palm away a Weligton header.
The Spanish side exerted more control in midfield after the interval, slowing down their opponents and making goal chances harder to come by.
Indeed it was not until the 65th minute, when Goetze broke down the right before shooting wide of the far post, that either side had a serious attempt on goal.
And yet a minute later, Weidenfeller made the save of the game as he blocked a rasping drive from Isco, leaving everything to be decided in the return.