Sonowal said he has asked the International Olympic Committee to issue guidelines on the wearing of turbans so that "such incidents do not take place again."
"We are aware that some players of the Indian basketball team were not allowed to play with turbans in the Asia Cup held in China recently," he said in a statement.
"We are shocked and outraged. We have spoken to Basketball Federation of India and sought a detailed report from them."
"Our government respects all religions and will do everything to ensure that their sentiments do not get hurt.
"Wearing a turban does not affect fair play and has not been objected to in international sports championships."
Amritpal Singh and Amjyot Singh were asked by officials to remove their turbans before the start of India's match against Japan on July 12 in Wuhan, saying they were breaking international basketball rules.
Despite team protests to the officials, the pair, who are both Sikhs, were not allowed on court with their turbans for the match and for all games during the tournament.
Amritpal, 23, told the Times of India newspaper he had always worn his turban for international matches and the "controversy left both of us distressed."
"Wearing turban is a part of me. When they told us we couldn't play with one it felt very awkward. But for the team we decided to play without turbans," said 22-year-old Amjyot.