His friend and colleague Jonathan Agnew said on Twitter: "Desperately sad to tell you that CMJ died peacefully this morning".
The news was also reported by the BBC, where Martin-Jenkins worked as a commentator on Test Match Special.
He also worked as a cricket correspondent for both the Daily Telegraph and the Times during his career.
Martin-Jenkins was given an MBE in 2009 and served as the MCC's president in 2010 and 2011. The official account of Lord's tweeted: "Former MCC President Christopher Martin-Jenkins has died. Sad, sad news to start the new year."
Martin-Jenkins' son Robin was a professional cricketer for Sussex until his retirement in 2010, making 162 first class appearances for the county.
Reacting to the news on Twitter, Charlotte Edwards, captain of England's women, said: "Awful news of Christopher Martin Jenkins passing away,true gentleman and fantastic servant to the game of cricket,he will be missed #ripcmj".
Former England spinner Shaun Udal added: "So sad to hear the news that Christopher Martin-Jenkins has passed away this morning. #ripcmj".
Ex-England all-rounder and current broadcaster Sir Ian Botham added: "Very sad to hear of the death of the 'Major'... Christopher Martin Jenkins. Our thoughts are with the family . A true Gentleman !!"
- Death & Funeral
- Sports & Recreation
- Christopher Martin Jenkins
- Jonathan Agnew