An injury to Karim Benzema added to a poor night for the visitors, whose mistakes were seized upon by the home team as Rodriguez and Arnold did the damage
Ricardo Rodriguez found the net from the penalty spot after Casemiro was adjudged to have fouled Andre Schurrle inside the area, before Arnold added a second midway through the opening half of the quarter-final first-leg tie at the Volkswagen Arena.
Madrid created a number of chances to pull one back, with Karim Benzema, Gareth Bale and Cristiano Ronaldo all threatening, but they were unable to beat goalkeeper Diego Benaglio for an important away goal.
Wolfsburg could even have made it three as they caused the visitors all kinds of trouble with their quick counter-attacks, but Schurrle failed to get his shot on target.
Madrid now face a tough task to turn things around when both sides meet again at the Santiago Bernabeu on April 12, after a disappointing display coming four days after their Clasico triumph at the home of fierce rivals Barcelona.
Ronaldo - who netted the winner at Camp Nou on Saturday - rightly had a goal disallowed for offside after only two minutes here, having found the net after a clever throughball from Benzema.
Benzema himself could have opened the scoring after turning Dante inside out in the Wolfsburg area, but Benaglio's trailing leg successfully kept out the Frenchman's low shot, with Bale blasting the rebound wide.
Rodriguez then earned Wolfsburg the lead in the 18th minute, coolly converting a penalty after Casemiro felled Schurrle as Madrid went a goal down for the first time during this Champions League campaign.
The opener served as a huge boost for Wolfsburg and Arnold doubled his side's lead just seven minutes later. Bruno Henrique sent in a low cross from the right and the Germany international beat Sergio Ramos to the ball before tapping home from close range.
Madrid created a number of chances to pull one back before half-time, with Benzema, Toni Kroos and Bale all going close.
Zinedine Zidane's men were then dealt another blow when Benzema was forced to leave the pitch due to injury shortly before the break, with Jese Rodriguez taking his place in attack.
Ronaldo looked to lead his team early in the second half, trying his luck from outside the box on two occasions, before heading over the bar after a fine cross from Bale.
Schurrle could have piled even more misery on the Bernabeu side halfway through the second period after a quick break, only to wildly fire over the bar from 10 yards out.
Benaglio again showed his class with 20 minutes left on the clock as he denied Ronaldo with a fine save after the Portugal star had been set up by substitute Isco.
Madrid pushed hard for an away goal in the closing stages of the game, but Wolfsburg held out for a famous victory, as Dieter Hecking's men stunned the 10-time champions and took a significant step towards the last four.
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