The spacecraft is expected to arrive at the ISS at 21:30 GMT on Sunday.
The Crew Dragon spacecraft has successfully entered orbit, Roscosmos said later in the day.
"The launch of the Crew Dragon spacecraft into the specified orbit and its separation from the second stage of the carrier rocket went normally," the space corporation said on Telegram.
The launch had been scheduled for September 26 but was delayed until September 28 due to Tropical Storm Helene.