He was 86 and is survived by his wife and two children.
His son, Ashok Singh, vice president of the Madhya Pradesh Congress Committee, said that the veteran Congressman suffered a heart attack late Saturday night and died before he could be rushed to hospital.
His last rites would be performed today in Gwalior, he informed.
Condolences poured in with Congress general secretary and former Madhya Pradesh chief minister, Digvijay Singh, describing him as a "close family friend".
The Leader of Opposition in the Madhya Pradesh Assembly, Ajay Singh, called Rajendra Singh a dedicated soldier of the Congress and said his death was an irreparable loss to the party in the state.