Kuwait Flight KU118 was travelling over Germany when it declared a state of emergency and has landed at Heathrow.
The plane has now landed at Heathrow airport, according to aviation website Air Live.
The Kuwait Airlines Boeing 777-200 was travelling from New York to Kuwait City.
The plane sent out an emergency signal as it travelled over Europe shortly after 8am and turned back over Germany.
Flight tracking data shows the Boeing 777 headed for Britain and landed at London Heathrow Airport at around 9.10am.
A spokesperson for the Metropolitan Police said: "It was a routine diversion for a medical emergency."
Ill passengers were taken off the plane and are being treated, a spokesperson for Heathrow Airport said, although she could not confirm their symptoms, according to a report in the Independent.
It had been due to land in Kuwait City at 9.25pm (BST) tonight.
Yesterday, at least 25 people were killed in Kuwait after a suicide bomber attacked a packed mosque during Friday prayers.
Islamic State have claimed responsibility for the explosion this morning at the Shi'ite Muslim mosque called Imam al-Sadeq Mosque.
The group said it had targeted a "temple of the rejectionists" – a term it usually uses to refer to Shi'ite Muslims, who it regards as heretics.