I couldn't find evidence of how he died. However, Babur died in Agra at the age of 47 on 5 January [O.S. 26 December 1530] 1531, and was first buried in Agra but, as per his wishes, his mortal remains were moved to Kabul and reburied in Bagh-e Babur in Kabul sometime between 1539 and 1544.