The man, 73, had just carried the torch about 600 feet before he was stricken, the New York Times reported. He was described as a Greco-Roman wrestling coach and school athletic director.
"He returned to the gathering place and was photographed, then said he was not feeling well and was taken to the hospital, but the doctors were unable to save him," Roman Osin, a spokesman for the torch relay, told reporters. "We express our deepest condolences to his loved ones."
The 2014 Winter Olympics are scheduled to begin Feb. 6 in the Black Sea resort of Sochi.
The organizers of the torch relay say it is the most ambitious ever. The flame has been taken into space, to the North Pole and underwater in Lake Baikal.
On Dec. 7, a 101-year-old Siberian man became the oldest participant in a torch relay ever when he carried the flame for 600 feet through the streets of Novosibirsk.
There have also been some embarrassments, including one incident where the flame went out. A disposable cigarette lighter was used to relight it.