The Londoners had salvaged a 1-1 draw late in the first leg at the Emirates last week, but were undone by goals in each half from the Frauen-Bundesliga leaders.
Former Gunner Jill Roord scored the opener after just nine minutes, hooking in from close range after the visitors failed to clear a corner.
The home side - playing at the men's team's Volkswagen Arena - thought they had netted again when Tabea Wassmuth stroked in but after a long check by VAR, it was ruled out for offside.
They did get a fortuitous second on 72 minutes when defender Leah Williamson inadvertently converted into her own net from Sveindis Jane Jonsdottir's low cross.
Arsenal pushed to find a way back into the tie but Vivianne Miedema's towering header struck the crossbar, before Williamson's follow-up was brilliantly tipped onto the post by goalkeeper Almuth Schult.
"We could have played better in the first half," said Gunners manager Jonas Eidevall. "We knew it would be a game of fine margins and it was, but we hit the bar, the post and they didn't go our way.
"They are very physical and demand a lot of opponents. I'm a little disappointed with certain aspects of our performance.
"They man-marked us and were very aggressive. We expected that but we were disappointed we didn't find the tactical balance."
Victory for two-time champions Wolfsburg sets up a tantalising semi-final against current holders Barcelona.
