The star, 75, has enjoyed a successful career with notable roles including Quentin Crisp in The Naked Civil Servant, the title role in The Elephant Man and a recurring role in the Harry Potter films.
He also played Bob Champion, the North Yorkshire jockey who won the 1981 Grand National on Aldaniti after his own battle with cancer.
In a statement, Sir John said: “I have always been open about the way in which I conduct my life and in that spirit I would like to make a statement.
“I have recently been diagnosed with early stage pancreatic cancer. I am undergoing treatment and am more than optimistic about a satisfactory outcome, as indeed is the medical team.
“I am continuing to focus on my professional commitments and will shortly be recording Jeffrey Bernard Is Unwell (one of life’s small ironies!) for BBC Radio 4.”
The actor has been nominated for two Oscars, for The Elephant Man and Midnight Express.
He enjoyed a big hit with sci-fi horror Alien in 1979.
The star was awarded a knighthood for services to drama in 2014.
Hurt has been busy in recent months, filming The History of Love with Gemma Arterton and Sir Derek Jacobi and the new Tarzan with Samuel L Jackson and Margot Robbie.
He also starred in a special 50th anniversary episode of Doctor Who.
He played Caligula in the celebrated BBC drama I, Claudius, and also made his name with a series of stage roles.
On the big screen, he played Mr Ollivander, a wand merchant, in several Harry Potter films.
Other recent movies include V for Vendetta (2005), Indiana Jones and the Kingdom of the Crystal Skull (2008), Tinker Tailor Soldier Spy (2011), and Hercules (2014).
Other roles have included his performance as Stephen Ward - a key figure in the Profumo affair - in Scandal and a reprisal of his role as Crisp for An Englishman In New York in 2009, 34 years after his original portrayal of the flamboyant figure.
Hurt’s distinctive voice has been used several times as narrator, and accompanied a chilling Aids awareness advertising campaign in the 1980s.
After going to art college, Hurt studied at Rada (Royal Academy of Dramatic Art) when he landed a scholarship.