The incident took place on Saturday afternoon and resulted in the collapse of the ceiling in the shrine.
"There are a number of visitors under the rubble, some of them alive, and we are communicating with them to follow up on their health status," Karbala Directorate of Civil Defense chief Taher Al-Zubaidi was quoted as saying by the Iraqi News Agency.
Rescue teams have managed to retrieve three children from under the rubble, who were taken to a hospital, the official said. Emergency services have delivered oxygen, drinking water and food to the people stuck inside the accident site by manually removing the rubble and concrete blocks, he said.
Civil defense sources told Al Arabiya broadcaster that eight people have been rescued and five still remain trapped under the rubble.
Meanwhile, the Iraqi News Agency reported, citing the Directorate of Civil Defense, that four bodies have been recovered from the under the rubble.
A rescue operation continues.