A spokesman for the Swedish team says the Washington Capitals forward will speak to the media later today.
Reports initially said he was suffering from a migraine headache. But Swedish Olympic Committee spokesman Bjorn Folin said the banned substance was in an allergy medication Backstrom has taken for seven years.
The Swedes lost the game 3-0 to Canada.
"It was a shocking message to get," goalie Jhonas Enroth told the Swedish news agency TT after the final. "We found out two hours before the match."
Backstrom, who had been the Swedes' No. 2 centre in the absence of Henrik Zetterberg and Henrik Sedin, had four assists in the first five games of the tournament.
Backstrom was not on the ice for pre-game warm-ups but was listed on the official lineup sheet.
Backstrom is the sixth athlete to fail a doping test at the Games. Five of the six, including Backstrom, tested positive for minor stimulants often found in food supplements.
With files from The Associated Press.