Officials said the balloons struck each other, then one fell the ground near the Ortahisar area of Urgup, Hurriyet Daily News reported.
Cappadocia is a tourist destination in the central Turkish province of Nevsehir.
Nevsehir Mayor Hasan Unver said balloon rides would fly on Tuesday.
"More people die while doing parachuting or rafting," Unver said. "The risks are lower in the balloon sector."