A stewardess said Dodds' fall was the result of his being extremely intoxicated, having drunk vodka the entire flight from the northern Russian city of Nadym.
"Alexander drank Beluga [vodka] almost all three hours of the flight, while not eating anything with it even once," she told Life News.
The flight was on a Tu-134 specially equipped for travel by a small number of VIP passengers, who were offered unlimited amounts of alcohol during the flight.
Dodds was hospitalized after the accident Saturday, but his condition quickly improved and he was set to be released on Monday, Life News reported.
Dodds is the head of upstream operations at oil company TNK-BP.