Ilya Kotik, who was travelling with the 64-year-old Czech leader, told state radio Havel had been suffering from a persistent bronchial problem for days and had several bouts of high temperature.
"I felt that it was best for him to leave, that it was not acceptable to continue with the journey," Kotik said.
Official Kuwaiti sources said earlier Havel left the Gulf Arab state aboard a private Kuwaiti aircraft, but some members of his delegation had stayed on for official talks.
Havel had been expected to hold a news conference on Monday morning, but it was called off at the last minute.
Kuwait's Emir Sheikh Jaber al-Ahmad al-Sabah visited Havel at the guest palace before his departure and wished him "a speedy recovery after suffering a sudden health indisposition," the official Kuwait News Agency reported.
Sheikh Jaber had held an official dinner on Sunday night for Havel who was seen shaking hands with scores of Kuwaiti ministers and prominent members of the ruling al-Sabah family.
Since 1993, the Czech president has suffered a series of grave illnesses including bronchitis and pneumonia. He lost a third of his lungs and nearly died in December 1996, after an operation to remove a malignant tumour.
A playwright, former dissident and former chain smoker, Havel was hospitalized three times last year, once for a cold, once for aggravated bronchitis and once for a hernia operation.
In April 1998, he underwent emergency surgery on a ruptured intestine in Innsbruck and almost died of complications when doctors operated to remove his colostomy bag three months later.