The three-stage carrier rocket was launched at 11.01 a.m. Moscow time (7:01 GMT) as planned, with the Soyuz TMA-13 spacecraft subsequently removing from the rocket, a RIA Novosti correspondent reported from the launch site.
The world's sole orbiter was successfully moved to a higher orbit October 4 to receive the Soyuz craft carrying the 18th ISS expedition - U.S. astronaut Mike Fincke, Russian cosmonaut Yury Lonchakov and U.S. space tourist Richard Garriott.
The crew was approved by Russia's space agency in late September after completing a series of preflight tests and medical checks.
The son of a U.S. astronaut, millionaire Garriott made his fortune in online computer games, including the popular Ultima Online, and paid $30 million to become the sixth space tourist to travel to the ISS.
He wants to conduct scientific experiments while onboard and some reports have said he may even conduct a space walk.