In the first grass court final of her career, the four-time Grand Slam winner Osaka was troubled by the injury and lost the opening set 6-1, having taken a short break for treatment after losing the first three games.
The Japanese sixth seed battled on but was visibly troubled by the injury, eventually signalling she would be unable to continue one game into the second set.
Muchova's victory continues a strong season for the 29-year-old Czech, who won the Qatar Open in February and made it to the final of the Stuttgart event in April.
The victory will return Muchova to the top 10, with the Czech to climb to ninth when the rankings are updated on Monday.
Despite being brought forward to 0900 GMT to beat the heat, the mercury was already at 36 degrees Celsius (96.8 Fahrenheit) when the players took to the court on Saturday.
A two-time winner on the hard courts of the US Open and the Australian Open, Osaka came into the match hoping to break through for a debut grass court title just days out from Wimbledon.
Osaka had been broken just five times in four matches on her way to the final but quickly found herself two breaks and three games down in the opening set, before seeking medical treatment.
The 28-year-old received treatment and returned, unleashing a stunning, back-spinning drop shot to win her first and only game of the set.
After losing the opening game of the second set on Muchova's serve, Osaka approached her coach and discussed the injury, before telling the umpire she would be unable to continue.
Wimbledon begins on Monday, with Muchova seeded 10th and Osaka 14th.