The Dutchman struggled with his game throughout and his usually dependable serve coughed up 13 double faults in the first-round defeat.
Krajicek is set to play top seed Lleyton Hewitt in the second round at Wimbledon after Tuesday’s draw.
“I’ve been struggling with my serve for six months now,” Krajicek said.
“My elbow just won’t allow me to serve too much in one day and I just can’t get the timing right.
“In the past, if I had a problem, I would just work on it for a couple of days and then it would be fine for months. I can’t do that now, so it’s doubly frustrating.”
A double fault from Krajicek on the opening point was an indication of what was to come.
Mutis, ranked 80th in the world, grew in confidence and after breaking in the ninth game, he served out to take the first set.
The second set followed the same pattern but Mutis faltered when he served for the match at 5-4, losing his serve to 15.
The set went into a tiebreak and more poor play from Krajicek, the 1996 Wimbledon champion, gave Mutis four match points. He saved the first two but the Frenchman clinched one of his best victories with an ace.
It was a good day all round for the French as Sebastian Grosjean and Arnaud Clement joined Mutis in round two, albeit in contrasting styles.
Grosjean, runner-up to Andy Roddick in the Stella Artois Championship, suffered a mid-match slump but regained his composure to beat German Philipp Petzschner 6-2 5-7 6-3.
Frenchman Arnaud Clement, a semi-finalist in Halle last week, cruised into the second round with a 6-2 6-3 victory over Dutch wildcard Fred Hemmes Jr.
Martin Verkerk, who stunned the tennis world by reaching the final of the French Open, plays his first match on grass against German Lars Burgsmueller later.
In the women’s event, fifth seed Nadia Petrova stuttered to a 6-4 3-6 6-2 win over Angelique Widjaja of Indonesia, while Barbara Rittner and Els Callens were among the first-round winners.
Top seed Kim Clijsters of Belgium opens her title bid with a second-round match against Cara Black of Zimbabwe.
Results (prefix number denotes seeding):
Men Frantisek Cermak (Czech Republic) beat Nicolas Kiefer (Germany) 6-3, retired 1-Jiri Novak (Czech Republic) beat Jurgen Melzer (Austria) 6-1 6-3 Jan Vacek (Czech Republic) beat Anthony Dupuis (France) 7-6 (7-2) 6-3 Sebastian Grosjean (France) beat Philipp Petzschnier (Germany) 6-2 5-7 6-3 Olivier Mutis (France) beat Richard Krajicek (Netherlands) 6-4 7-6 (7-4) 7-Arnaud Clement (France) beat Fred Hemmes Jr (Netherlands) 6-2 6-3
Women 5-Nadia Petrova (Russia) beat Angelique Widjaja (Indonesia) 6-4 3-6 6-2 Barbara Rittner (Germany) beat Rita Grande (Italy) 6-1 6-3 Els Callens (Belgium) beat Cho Yoon-jeong (South Korea) 6-4 6-1 Maria-Antonia Sanchez-Lorenzo (Spain) beat Nicole Pratt (Australia) 7-5 6-2.—Reuters