The Belgian, last year's winner, showed no ill effects of her left wrist problem as she won the first 20 points of the match before clinching the first set in just under 30 minutes.
Kremer, ranked 140th in the world and who surprisingly beat the former world number one in their only other meeting in Berlin in 2001, was no match for her opponent this time.
Clijsters will now face Martina Muller in the second round after the German beat Ukrainian Katerina Bondarenko 2-6, 6-4, 6-4.
There were mixed emotions for two other Belgians as Caroline Maes came from behind to beat Ukrainian Yuliana Fedak 3-6, 6-2, 7-5 in their first round match, while Kirsten Flipkens lost 6-3, 6-4 to Russia's Vera Zvonareva in the second round.
Michaella Krajicek of the Netherlands won the day's opening match when Italian Mara Santangelo was forced to retire at 5-2 down in the first set after damaging her wrist.