Murray, number three seed and reigning US Open winner, claimed the match 6-4 6-1 6-2.
"Today was the best I've played here," said Murray straight after his win.
"I've struggled in the last few rounds a little bit.
"Jeremy has had a great tournament - he's beaten some top players.
"I had to come out sharp and get off to a good start."
Murray advances to the semi finals and will face the winner of Wednesday night's quarter final between Swiss master Roger Federer and another Frenchman, Jo-Wilfried Tsonga.
Chardy at times challenged Murray but could not match the polish of his classy opponent, who has made the final of the Australian Open twice before.
The Frenchman, ranked 36 in the world, broke Murray in the third set, before eventually going down 6-2.
Murray described his emphatic win as the best of his tournament so far.
The British star needed only one hour and 51 minutes to see off Chardy's challenge and set up a semi-final date.
Murray, the reigning US Open champion, has yet to drop a set in five matches at Melbourne Park this year.
The loss brought to an end the 25-year-old Chardy's best grand slam campaign.
He had beaten seeds in each of the previous three rounds, with his best victory the tough five-setter over No.6 Juan Martin del Potro from Argentina in the third round.
- With AAP