Muchova broke 29-year-old Boulter’s serve twice in the first set and only needed one more in the second set to go 6-5 ahead before she wrapped up the victory.
Elsewhere, British number four Fran Jones also exited the tournament, retiring in the second set of her match with American Jessica Pegula through illness.
Jones, 25, had knocked out Venus Williams in the first round despite feeling under the weather but struggled against Pegula.
Pegula had won the first set 6-1 and despite a medical timeout Jones, who was seen coughing several times during the match, decided at 3-0 down in the second set she was not well enough to continue.
“I didn’t want to lose the opportunity to play Venus, but it’s a whole different ball game playing Jess,” Jones said.
“You need to be 10 out of 10 to compete against her and I’m probably a four out of 10 today. If I’m not able to give my everything out there, I don’t see the point when I’m already battling my general fitness as it is.”