Second-half goals by Ghanaians Kevin-Prince Boateng and Sulley Muntari left Barcelona with a huge task in the second leg after a night when Lionel Messi was conspicuously quiet for the Catalans.
Barcelona were fuming about the first goal when the ball appeared to strike the hand of Cristian Zapata before it ricocheted into the path of Boateng to fire home in the 57th minute.
La Liga leaders and Copa del Rey semi-finalists Barcelona, who failed to score for only the second time this season, dominated the first half in typical fashion but struggled to get past Milan's two lines of four defenders.
The Catalans' starting line-up featured 10 players from their youth academy and nine internationals with world and European champions Spain.
Milan's approach was much more haphazard as they struggled to string passes together, lost possession in key areas of midfield and thumped hopeful balls forward.
"The result is what it is. We had the game under control, although admittedly we didn't create too many clear chances and neither did they," Barcelona's interim coach Jordi Roura, standing in for Tito Vilanova who is recovering from throat surgery, told a news conference.
"We hoped we could wear them down. Their first goal was an isolated attack following a shot and a rebound."
"It's a bad result but I'm absolutely convinced that we can turn this around in the second leg with the support of our crowd."
"The boys deserved this result. They didn't give anything away at a defensive level and they made the most of the we had," he said in his usual monotone.
"We made some mistakes in the first half but we improved a lot in the second... the tie is very open."
El Shaarawy should have done better when he was sent clear by Kevin-Prince Boateng's flicked pass but failed to control the ball as he raced towards goal, allowing Carles Puyol to intercept.
Barca, who could have had a penalty when Dani Alves' whipped cross clearly hit Philippe Mexes' outstretched arm, took control with their familiar slick passing.
