"His wife, family and bandmates are all saddened by the loss of their loved one and one of the world's finest guitarists," the statement read, adding that Winter died on Wednesday.
Swiss police told AFP that Winter was found dead early Wednesday in a hotel room in Bulach, a small town north of Zurich, which lies close to the city's airport.
A Zurich police spokesman said the local prosecutor's office has ordered an autopsy to determine the cause of death.
"Based on the initial elements of the investigation, it appears that this death was the result of medical reasons, and that nothing points to the involvement of another person," the spokesman told AFP.
Winter, who was also a singer, was one of the most striking figures on the blues scene.
An albino who was heavily tattooed, his fragile frame and long blond hair contrasted starkly with his powerful, gravelly voice.
Born John Dawson Winter III in Texas in 1944, Winter was the son of a cotton farmer.
Winter began playing the clarinet aged five, switching to the ukelele and then the guitar a few years later.
According to his official website, he formed his first band when he was 14 years old, with his 11-year-old brother, Edgar, also an albino.
His big breakthrough came in 1968 when Rolling Stone magazine dubbed the guitarist the hottest item after Janis Joplin in an article about the Texas music scene.
After the 1969 Woodstock festival, Winter withdrew from the public eye because of a drugs problem before returning to the scene in 1973.
He had been on tour this month, most recently performing at the Cahors Blues Festival in France on July 14th.
He had been due to begin a US tour in August, ahead of the September 2nd release of his new album "Step Back", which features music icons such as Ben Harper, Eric Clapton and Dr. John.
Check Winter's Facebook page here.