Live television pictures showed a Soyuz spacecraft taking off fromthe Baikonur Cosmodrome in Kazakhstan, carrying three astronauts whowill deliver the torch to the International Space Station (ISS).
The flight to the ISS is expected to take about six hours.
On Saturday, two astronauts are due to take the torch on a spacewalk for the first time in Olympic history.
The Sochi Winter Olympics are due to begin on February 7 next year.