Clijsters sent an ominous warning to her rivals ahead of this month's Australian Open as she took just 60 minutes to dispose of Molik, who has been her friend since they were teenagers starting out on the junior circuit.
Former Australian Open finalist Marcos Baghdatis of Cyprus was made to work much harder in his 7-5, 7-5 first round win over American Mardy Fish.
"It wasn't my best match but I am happy," Baghdatis said.
"In the off season I worked hard on my fitness. I am quicker, fitter and I am enjoying it," he added.
Baghdatis will meet Czech Thomas Berdych in the second round after the fourth seed defeated Australia's Nick Lindahl 6-2, 6-4.
American James Blake beat fifth-seeded compatriot Sam Querrey 4-6, 6-3, 6-4 while Australian wildcard Carsten Ball defeated German Mischa Zverev 7-5, 6-1 to set up a meeting with top seed Andy Roddick.