Brightman, who began her training in Russia's Star City in January for a ride aboard a Russian Soyuz capsule and 10-day stay on the station, postponed her plans.
"Ms Brightman said that for personal family reasons her intentions have had to change and she is postponing her cosmonaut training and flight plans at this time," a statement shared on the Grammy winner's Facebook page said.
Brightman, 54, was to be the eighth paying tourist to visit the station, a project of 15 nations.