The morning accident happened in the town of Wittelsheim in eastern France during the 14th stage, a 124-mile route from Colmar to Besancon, the Interior Ministry said.
Lt. Col. Thierry Renard said by phone the motorcycle driver was a member of the Republican Guard and was unable to avoid the woman. He could not confirm reports that two other people were injured.
Commander Christophe Blanc told France Info radio the driver fell off his bike, which then hit and injured two others, although their lives were not in danger. One of the injured was a mother with a child in her arms, but the youngster was not hurt.
"No child or baby has been injured," Renard said. "We don't have any problem of that sort."
Deadly accidents are rare on the Tour de France. One boy was killed in 2000 and another in 2002 after being hit by sponsors' vehicles. Tour organizers then reduced the numbers of sponsor vehicles allowed on the course.
Interior Minister Brice Hortefeux expressed condolences to the victim's family. Hortefeux also ordered a police inquiry and reminded spectators to take all precautions to avoid accidents.