The attackers were dressed as women in black robes when they attacked on Friday, two inside the mosque and one just outside, a police official said.
Some police sources said the suicide bombers were women; others said they were a woman and two men dressed as women.
The attack also wounded 158 people.
The mosque complex belongs to the Supreme Council of Islamic Revolution in Iraq (SCIRI), the most powerful group inside Iraq's ruling Shia alliance.
Jalal al-Deen, a SCIRI leader, who was at the mosque during the explosions, said: "The Shiites are the target and it's a sectarian act. There is nothing to justify this act but black sectarian hatred."
He accused some Sunni newspapers of inciting violence by publishing reports that the mosque contained a detention centre where Sunnis were abused.
Many people were wounded and
taken to hospital
Jawwad Kathim, a firefighter, said: "This is a cowardly act. Every time I see these bloody scenes it tears apart my heart."
The attack came a day after a car bomb exploded near a Shia shrine in the southern city of Najaf, killing at least 13 people.
A member of the Baghdad city council appealed to Iraqis on state television to give blood.
Sheikh Jalaluddin al-Saghir, the prayer leader at the mosque and a Shia member of parliament from the United Iraqi Alliance, said that at least one of the bombers was dressed as a woman.
"Preliminary investigation shows that a woman, or a man dressed as a woman, managed to reach the security post of the female section, where the suicide bomber blew himself up causing panic and a rush by people to get out, allowing the two other terrorists to penetrate the mosque," he said.
One victim, Naba Mohsin, said: "My house is opposite to the mosque and when we heard the first huge blast I ran to make sure my father, who was praying there, is safe.
"When I entered the mosque, a second huge blast occurred and I saw a big blast with flames, I was thrown, then I woke up in the ambulance. I want to know if my father is alive."
Also in Iraq on Friday a Shia tailor was shot dead by armed men inside his shop in the al-Zab area about 70km (40 miles) southwest of the northern oil city of Kirkuk, police said.
The US military reported that one of its soldiers had been killed on Thursday when his patrol was hit by a roadside bomb near town of Baiji, 180km north of Baghdad.