Bouchard, the 18th seed, was all over the Kerber serve from the off and the left-handed German was caught cold. She was 5-0 down before she could draw breath in the face of the Canadian's accuracy, movement and variety of shot.
The first set went by in 23 minutes - Bouchard winning it with a forehand down the line - but Kerber's serve remained her weak point and she was broken in the third and fifth game of the second set.
The German ended her disappointing display by hitting a Bouchard second serve long.
"I just felt good," Bouchard said. "I think I executed my game plan really well. I was really mentally prepared for anything, for a battle. I'm confident and I really believe in my skills. I believe I can play with the best girls out there."
The 20-year-old next plays claycourt specialist Carla Suarez Navarro of Spain, the 14th seed, in the last eight.
Bouchard reached the semi-finals at this year's Australian Open, when she lost to eventual champion Li Na, and won her first WTA title on May 24 in Nurnberg, on clay.
Kerber managed to win just 28% of points on her second serve, but Bouchard's all-round game was far superior in front of a three-quarters empty Philippe Chatrier showcourt.
The German held her first service game of the second set, but hit long to lose her second, and failed to convert her one break point in Bouchard's next service game, when the Canadian struck a backhand into the corner to reach deuce.
Two double faults and a couple of errors meant Kerber's third service game of the set went in Bouchard's favour and the match was over after just 52 minutes.
In their only previous meeting, at last year's US Open, Kerber won in three sets.
"It was not my best day," said Kerber. "I was trying, but I had no rhythm. I made so many mistakes, I was not moving."