The affected athletes, comprising judokas, boxers, hockey players and those from track & field, have been shifted to a local hospital.
SAI has a National Centre of Excellence (NCOE) residential wing in Bhopal.
Last week, SAI had conducted 250 tests. Initially 18 men, including 10 judokas, tested positive. Later, 15 women also tested positive for Covid-19.
"Training has been temporarily stopped since Monday. All those players who tested negative have been told to stay inside the hostel and not to venture outside. We only go to the dining room for meals," a player from Bhopal told IANS on phone.
Judokas have been hit the hardest.
"The coach of the judo team is also among those who tested positive. A judoka selected for the ongoing Asian Olympic qualification tournament in Bishkek too tested positive. He was dropped from the national team," said a national level player.
Earlier this month, SAI had conducted RT PCR Covid-19 tests for the trainees of the NCOE and Olympic-bound athletes at Patiala and Bengaluru.
Of the 313 tests conducted in Patiala, 26 athletes tested positive. Four returned positive results in Bengaluru.
The national boxing coach C.A. Kuttappa was among the 12 boxers who tested positive for the virus.