In an event reduced to 54 holes by bad weather, Levy sank a winding 20-yard putt on the second extra hole to secure his third European Tour title.
Fisher, who also won this event in 2008, had hit a seven-under-par 64 to set up the play-off after Levy bogeyed his final hole for a two-under 69.
Martin Kaymer, part of Europe's Ryder Cup team, finished five shots back.
Levy, who went into the final round with a four-shot lead after 36 bogey-free holes, admitted he struggled to deal with the pressure of leading.
The 26-year-old carded three bogeys in his first five holes, then put his second shot into the spectators' area on the 18th.
"I didn't play really good on the front nine. I was thinking about the score and not on my own game," he said.
"I stayed patient and I started to play really good on the back nine."
Fisher, 35, was pleased with his putting, as he sank seven birdies in a bogey-free final round in Bavaria.
"I felt like I played pretty flawless on the front side, and kept it going on the back," the Englishman said.
"I didn't leave one short which is a positive sign."
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France's Alexander Levy beat England's Ross Fisher in a play-off to win the European Open in Bad Griesbach.