Anousheh Ansari, 40, an Iranian-American telecommunications entrepreneur, joined a Russian cosmonaut and a US astronaut in the Soyuz TMA-9 for a flight to the International Space Station (ISS) on Monday.
The Soviet-designed spacecraft lifted off into a clear blue sky at 0409 GMT from the Baikonur Cosmodrome in Kazakhstan.
"The flight is normal, the crew feel fine," a flight controller at mission control near Moscow said.
Unlike American Michael Lopez-Alegria and Russian Mikhail Tyurin, who are starting a six-month stint in space, Ansari will return to earth in 10 days with the outgoing US-Russian crew.
Ansari, a US citizen based in Dallas, Texas, who left Iran in 1984, has said she wants to be an example to her compatriots.
"I think my flight has become a sort of ray of hope for young Iranians living in Iran, helping them to look forward to something positive, because everything they've been hearing is all so very depressing and talks of war and talks of bloodshed," Ansari said last week.
But she was told to remove an Iranian flag from her spacesuit and, at the insistence of the Russian and US governments, promised that there would be no political messages during her trip.
Looking relaxed and smiling at a pre-launch news conference at the Baikonur Cosmodrome on Sunday, Ansari said she would still pack an Iranian flag for her trip.
A video grab of the Soyuz rocket
lifting off in Kazakhstan
Ansari has not said how much her ticket cost but previous space tourists have paid the Russian space programme about $20 million.
She had originally been scheduled to join a later Soyuz mission but took the place of Japanese businessman Daisuke Enomoto when Russian space officials said last month he was not able to fly for unspecified medical reasons.
Several hours before the Soyuz blast off, the US space Shuttle Atlantis undocked from the ISS.
The Soyuz craft will dock with the space station early on Wednesday. Atlantis is scheduled to land at the Kennedy Space Centre in Florida a few hours later.