Video published by Roscosmos showed the Soyuz blaster launching against grey and cloudy skies at 0607 GMT.
"The Soyuz-2.1a carrier rocket with the Fregat upper stage and 38 spacecraft from 18 countries took off from the Baikonur cosmodrome," Roscosmos said on its Twitter account.
The rocket will place in orbit 38 satellites from more than a dozen countries, including South Korea, Japan, Canada, Saudi Arabia, Germany, Italy and Brazil.
Among them is the Challenge-1, the first satellite made completely in Tunisia, which was created by the Telnet telecommunications group.
The launch was twice postponed from Saturday after a surge in voltage was detected.
