Warnapura worked as a commentator and cricket administrator following his retirement, serving as Director of Cricket Operations at Sri Lanka Cricket.
He leaves behind his wife, daughter, two sons and grandchildren.
"He was an excellent cricketer, administrator, coach, commentator and, above all, a good person, and his passing away is a huge loss for the cricket community," Sri Lanka Cricket President Shammi Silva said in a statement.
"I am sure his name and deeds will remain in our hearts forever."
Sri Lankan batter Lahiru Thirimanne posted: "Deeply saddened to hear about passing of the 1st test captain in Sri Lanka Sir Bandula Warnapura. Honoured to got to know him as a True gentleman. Condolences to his family in this tough time."
Former Test captain Mahela Jayawardena wrote: "It's Sad to hear the news of SL first test captain Bandula Warnapura's demise after a brief illness. Thoughts are with his wife and children. He coached me at Nalanda and was a steady influence in my growth as a cricketer and a person. May you attain Nibbana Sir."
Sri Lankan great Sanath Jayasuriya tweeted: "It is a sad day that the first test captain Bandula Warnapura has played his last innings. RIP we will miss you sir."
The Sri Lankan national men's side wore black arm bands during its T20 World Cup victory over Namibia on Monday evening as a tribute to Warnapura.