The rare illness affects the cells that release hormones into the bloodstream. Mr Khan did not give any further details of his condition.
He had tweeted on 6 March that he was suffering from a “rare disease” but did not say what it was.
Khan, 51, has acted in more than 100 films including Bollywood hits Piku, Maqbool, Haasil and Paan Singh Tomar.
His English language films include Life Of Pi, Jurassic World, Slumdog Millionaire and The Amazing Spider-Man.
He took to Twitter on Friday to talk about his illness.
His wife, Sutapa Sikdar, had said in a Facebook post on 10 March : “My best friend and my partner is a ‘warrior’ he is fighting every obstacle with tremendous grace and beauty.”
Health experts say neuroendocrine tumours can develop in many different organs in the body and can be cancerous or non-cancerous.
Some tumours can cause abnormally large amounts of hormones to enter the bloodstream and cause symptoms such as heart problems, changes in blood pressure or cramps.
Some neuroendocrine tumours can be treated through surgery or chemotherapy.
Khan is India’s best-known international actor and has also featured in a wide range of well-received roles in Bollywood and independent Hindi films.
In 2013, he won India’s National Film Award for his leading role in Paan Singh Tomar, a biopic about a top athlete who becomes a bandit.
He has also won the Viewers’ Choice Award at the Cannes Film Festival for his portrayal of a lonely accountant who mistakenly receives a lunchbox intended for a colleague in the 2013 film The Lunchbox.
It was also the only Indian film to be selected for competition at the London Film Festival that year.