The Botswanan, who won the world title in 2011 and finished second behind Christine Ohuruogu in Moscow last year, tested positive for the banned stimulant methylhexaneamine after the final of the 400 metres in Glasgow.
Montsho, 31, who struggled to finish fourth in the final, will have her B sample tested on Monday. She has been provisionally suspended.
A statement from the Commonwealth Games Federation (CGF) said: “In accordance with the CGF anti-doping standard for the Commonwealth Games, the CGF federation court conducted a provisional hearing this afternoon to consider an adverse analytical finding submitted by Amantle Montsho of Botswana, after the women’s 400 metres final on July 29.
“The athlete’s A sample was found to contain methylhexaneamine, prohibited as a stimulant under class s6 of WADA’s Prohibited List.
“Ms Montsho was notified of her A sample result and has asked for her B sample to be tested, which will take place at the accredited laboratory in London on Monday August 4.”
One of Montsho’s main rivals over 400m was Christine Ohuruogu, the current world 400m champion and former Olympic and Commonwealth gold medallist.
After competing in the women’s 4x400m relay on Saturday, Ohuruogu said: “I heard about it (the doping case) just before we came out.
“I didn’t want to think too much about it. My initial reaction was desperate disappointment, but I think I need to find out exactly what happened before I talk too much about it.”
Montsho is the most high profile athlete to have failed a drugs test at the Games, which have also seen 16-year-old Nigerian weightlifter Chika Amalaha stripped of her gold medal.
Montsho arrived in Glasgow as defending Commonwealth 400m champion, but she could only finish fourth behind a Jamaican cleansweep led by Stephanie McPherson.
The three-time African champion is a mainstay on the Diamond League circuit and her victory at the 2011 Daegu worlds saw her become Botswana’s first world or Olympic track and field champion.