"Saini was admitted in the hospital on June 22. He passed away today (Monday) evening around 7 p.m," an AIIMS official told , adding that the BJP leader was "having some blood-related issues".
Saini was appointed as the party's Rajasthan chief last year, months before the state went to assembly polls.
Prime Minister Narendra Modi, Home Minister and BJP chief Amit Shah and Rajasthan Chief Ashok Gehlot condoled the death of Saini.
"The passing away of Shri Madanlal Saini Ji is a major loss for the BJP family. He contributed to strengthening the Party in Rajasthan. He was widely respected for his congenial nature and community service efforts. My thoughts are with his family and supporters. Om Shanti," the Prime Minister tweeted.
"Just received the saddening news of Madan Lal Saini's death. Saini, who held several posts in the party was a true public servant whose whole life was devoted to the party and society. He was instrumental in strengthening the BJP in Rajasthan.
"The demise of Madan Lal Saini is an imperfect loss to the BJP family. I express my condolences to the bereaved family in this hour of grief and pray to the Lord for the peace of the departed soul," Amit Shah said in a series of tweets.
"Shocked and saddened to hear about the passing away of Madan Lal Sainiji, President of BJP Rajasthan. My thoughts and prayers are with his family members. May God give them strength to bear this loss. May his soul rest in peace," Gehlot tweeted.
( With inputs from IANS )