Rescuers removed rubble using a bulldozer in their search for survivors on Monday after the incident at the Qattarat Al Imam Ali shrine near Karbala, about 80 kilometres south of Baghdad.
Five women, two men and a child were among the dead, Iraq's civil defence said on Monday.
Six people were rescued from the rubble, it said.
The civil defence said the ceiling of the shrine caved in when the landslide hit on Saturday, dumping a torrent of rock and mud inside the structure, which lies in a natural depression.
The entrance, walls and the minarets of the shrine, which was built at the location of a water source in the desert, remained standing.
“Rescue operations continued for more than 60 hours day and night since Saturday, which resulted in the exhumation of eight bodies, including five women, a child and two men,” said a civil defence statement.
The area of the Qattara shrine is now closed following an agreement with the Governorate of Karbala “due to the fragile pillars and the danger of the shrine poses to the public following the incident”, the statement said.
“Rescue officers ensured that communication with survivors was ongoing while providing them with oxygen, drinking water and food.”
A total of 30 teams with “high level of scientific and field experience” gathered from across the country to search for survivors, the statement said.
Earlier, Jawdat Abdelrahman, director of the civil defence media department, told AFP that three children had been rescued and taken to hospital.
Civil defence spokesman Nawas Sabah Shaker had said on Sunday that between six and eight pilgrims were trapped under the rubble.
The three children rescued earlier were in a “good condition” and being monitored in a hospital, emergency services said on Sunday.
The civil defence said they removed the shrine’s gate to open a space for rescue equipment at the site.
The cause of the landslide was not immediately known.
“We want to know what happened, why it happened,” said Bassem Khazali, whose nephew was among the victims.
However, the civil defence blamed high humidity for the incident.
Shiite cleric and political leader Moqtada Al Sadr said “suspected corruption … caused civilian deaths”, in a post on Twitter on Sunday evening.
But Iraq's Shiite waqf, which is responsible for administering Shiite properties in the country, said it did not manage the shrine nor the land on which it was built.
“The shrine does not belong to a known party but to individuals who have been summoned [for questioning],” Karbala governor Nassif Al Khatabi wrote on Facebook, without providing further details.
Mr Al Khatabi said the area would be closed pending an investigation.
Iraq is mired in a months-long power struggle between rival Shiite blocs that has further weakened the country’s caretaker government and its ability to provide basic services.