Montsho, who finished fourth in the women's 400m final on Tuesday, provided a positive A sample that contained the prohibited stimulant methylhexaneamine.
The 31-year-old, who won gold at the Commonwealth Games in New Dehli four years ago, has been provisionally suspended and asked for her B sample to be tested.
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Montsho is the second athlete to fail a doping test at the Games after Nigerian teenager Chika Amalaha was stripped of her weightlifting gold medal on Friday.
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