Vinesh's outburst comes after the United World Wrestling provisionally suspended the Wrestling Federation of India for not conducting elections on time.
Vinesh's injury clears the way for Antim Panghal's inclusion in the squad.
Around 150 people, including family members of the wrestlers, are seeking a meeting with IOA president P T Usha and ad-hoc panel chief Bhupender Singh Bajwa.
The move to exempt Bajrang and Vinesh, however, has not gone down well with fellow competitors, who have threatened to move court.
The decision was conveyed to the organisers as well as the Sports Authority of India.
Vinesh took to Twitter to post the famous poem written by Pushyamitra Upadhyay.
National football team captain Sunil Chhetri and former Indian cricketer Irfan Pathan too criticised the action against the wrestlers.
Delhi Police cleared the sit-in site of the protesting wrestlers at Jantar Mantar after a march to the new parliament building ended up in a scuffle.
The police said that 700 people were detained across the national capital.
Thousands of police personnel have been deployed in Lutyens' Delhi, no permission granted to hold 'Mahila Mahapanchayat'.