Kvitova lost the opening game in her match against the 16-year-old Barty, but then won six straight in the first set and again raced through the second set despite being broken once.
"She has a big serve with kicks and good forehand," Kvitova said of the Australian teen. "She has very good touch."
The left-handed Czech won her first Grand Slam title at Wimbledon last year, and then won the WTA Championships. Although she has yet to win a title in 2012, she is seeded fourth at Roland Garros and is expected to make it deep into the tournament.
Barty is the youngest player in the draw at the French Open, one of only eight teenagers entered. The Australian received a wild-card invitation to compete in Paris.
"It was tough out there today," Barty said. "I didn't play my best tennis, but she didn't allow me to. I was out there giving it my all, but unfortunately just didn't come out on top today."
The oldest player in the draw, 41-year-old Kimiko Date-Krumm of Japan, lost to 2010 French Open champion Francesca Schiavone of Italy 6-3, 6-1.
Copyright 2012 The Associated Press. All rights reserved. This material may not be published, broadcast, rewritten or redistributed.