The incidents are understood to be separate and unrelated, with one arrest in the city centre and the other in the west end.
Both occurred late on Saturday.
One of the officials held is believed to be the Indian Olympics Association (IOA) secretary general Rajeev Mehta, who is part of the Indian contingent at the Commonwealth Games.
The other has been named by Indian media as wrestling referee Virender Singh Malik.
The men are expected in Glasgow Sheriff Court tomorrow.
A spokeswoman for Police Scotland said: "On Saturday, August 2, a 49-year-old man was arrested on suspicion of assault in Glasgow city centre and a 45-year-old man was held for alleged assault in west Glasgow.
"Both men are expected to appear at Glasgow Sheriff's Court on Monday."
The Indian High Commission in London was reported in The Times of India as saying: "We have learnt about the detention of two members of the Commonwealth contingent by the local police.
"Our consulate in Edinburgh has deputed an official to Glasgow to keep in close touch with the police to ascertain full facts of the case. We are also in touch with the team."
Both men were staying in hotels around the city centre and are not part of the official 215-strong Indian contingent staying in the Games Village in the Dalmarnock area.