At 18:14 GMT (00:14) local time, the rocket took off with a Progress MS-10 spacecraft carrying supplies to the International Space Station (ISS).
The first manned mission to the ISS since the failure is due to take off at the beginning of December.
Russia, the only country able to ferry astronauts to the space station, suspended all launches after a Soyuz rocket failed on October 11 just minutes after blast-off. "The takeoff of the Soyuz-FG rocket is set for 1814 GMT", Russian space agency Roscosmos said in a statement.
The faulty sensor "was damaged during the assembling of the strap-on boosters with the core stage (the Packet) at the Baikonur Cosmodrome", according to Oleg Skorobogatov, the Central Research Institute of Machine Building deputy director general and head of the investigation committee.
Since the October mishap, two Soyuz rockets were launched successfully from Plesetsk in northwestern Russian Federation, while a third lifted off from French Guiana carrying satellites into orbit. This launch was the first rocket of this type after the accident on October 11. The cargo ship will deliver to the ISS about 2.5 tons of various cargoes, including fuel, water and compressed gases. Northrop Grumman will launch another cargo shipment in a Cygnus capsule, powered by an Antares rocket, early Saturday morning (Nov. 17). Any longer than three months would have meant the current crew would have to return to Earth and the ISS would be vacant for the first time in more than 16 years.
Speaking at a news conference in Star City near Moscow, McClain said that occasional failures were inevitable, but that the mishap with the Soyuz-FG in October had demonstrated the reliability of its emergency safety mechanisms. "We're ready to fly", she said. A lot of people called it an accident or an incident, or maybe want to use it as an example of not being safe.