He was 92.
His family said he passed away at 10:45 AM at the Army Research and Referral hospital.
He was first admitted to the base hospital here on November 1 with a fracture in his femur bone and ribs and was later shifted to the R and R hospital after some complications developed.
He is survived by his wife, son and IFS officer Y K Sinha who is at present Indian Ambassador to Sri Lanka and is moving for his new posting to the UK, and three daughters.
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Sinha has served as the Jammu and Kashmir Governor and led the first batch of Indian troops who entered J and K when Pakistan raiders invaded in 1947.
He resigned from service after the government superseded him and appointed General A S Vaidya as the new army chief.
Lt Gen Sinha had joined army in 1943 and has also served as India's Ambassador to Nepal and as the Governor of Assam.
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Former J-K Chief Minister Omar Abdullah wrote on twitter, "Very sorry to hear of the demise of Lt Gen Sinha, former Governor of J&K. May his soul rest in peace. My condolences to his family."