Police in Isfara told RFE/RL on November 4 that Umedjon Tojiev jumped from a third-floor window on November 2 and broke his leg.
He was officially being charged with organizing a criminal group.
Tajik Interior Minister Ramazan Rahimov has ordered an investigation into the incident.
Tojiev was initially arrested on October 30 for refusing to follow police instructions.
His colleagues and relatives say the charges against him are politically motivated and that he might have been tortured while in custody.
The deputy chairman of the HNIT, Saidumar Husaini, told RFE/RL that party representatives have been sent to Isfara to clarify the situation.