Phyllis Main, from Glasgow, had been staying in Acapulco while taking part in the nine week course.
The 62-year-old was taken to hospital during the trip and it is not known if her illness was linked to yoga.
Phyllis travelled from Scotland to Mexico on October 3 and took part in the course along with hundreds of other participants.
The Mail on Sunday reported she fell ill with stomach pains.
She had kept her friends and family up to date with her travels on social media, writing: "Acapulco tomorrow to become a Bikram Yoga teacher love this yoga if it’s not 90 mins it’s not Bikram Yoga.
"Will miss you all."
Bikram yoga is hugely popular worldwide.
A Foreign and Commonwealth spokesman said: “Our staff are providing consular support to the family of a British woman who died in Mexico”.