Karim Khazim, the city's chief health official, said the 32 killed included seven Iranians.
Police said the attacker was a woman but provided no other immediate details. Karbala is located about 50 miles south of Baghdad.
Also Monday, two U.S. soldiers were killed when their Humvee hit a roadside bomb. The soldiers were clearing a road in northern Baghdad when they were killed, the military announced. At least 3,990 members of the U.S. military have died since the beginning of the Iraq war in March 2003, according to an Associated Press count.
Elsewhere in the capital, Vice President Dick Cheney and Sen. John McCain vowed in meetings with Iraq's prime minister that the U.S. would maintain a long-term military presence in Iraq until al-Qaida is defeated there.
Explosions went off near the heavily fortified Green Zone shortly after Cheney arrived. Helicopter gunships circled central Baghdad, but no details were immediately available on the cause of the explosions.
The presumptive Republican candidate for president, who has linked his political future to military success in Iraq, met with Prime Minister Nouri al-Maliki shortly before the Iraqi leader began separate talks with Cheney.
Al-Maliki said he and the vice president discussed ongoing negotiations over a long-term security agreement between the two countries that would replace the U.N. mandate for foreign troops set to expire at the end of the year.
"This visit is very important. It is about the nature of the relations between the two countries, the future of those relations and the agreement in this respect," the prime minister told reporters. "We also discussed the security in Iraq, the development of the economy and reconstruction and terrorism."
McCain stressed that it was important to maintain the U.S. commitment in Iraq, where a U.S.-Iraq military operation is under way to clear al-Qaida in Iraq from its last urban stronghold of Mosul, 225 miles northwest of Baghdad.
"We recognize that al-Qaida is on the run, but they are not defeated," McCain said after meeting al-Maliki. "Al-Qaida continues to pose a great threat to the security and very existence of Iraq as a democracy. So we know there's still a lot more of work to be done."
McCain, who arrived in Iraq on Sunday, told reporters that he also discussed with the Shiite leader the need for progress on political reforms, including laws on holding provincial elections and the equitable distribution of Iraq's oil riches.
At a news conference with U.S. Ambassador Ryan Crocker and Gen. David Petraeus, the top commander in Iraq, Cheney said that given the nearly 4,000 U.S. troop deaths and billions of dollars spent on the war, it is very important that "we not quit before the job is done."
Cheney credited reductions in violence to President Bush's decision to deploy an additional 30,000 troops to the war zone. He said one of Bush's considerations in whether to draw back more than the 30,000 before he leaves office will be whether the U.S. can continue on a track toward political reconciliation and stability in Iraq.
"It would be a mistake now to be so eager to draw down the force that we risk putting the outcome in jeopardy," said Cheney, on an unannounced visit to Iraq. "And I don't think we'll do that."
Violence has dropped throughout the capital with the U.S. troop buildup as well as a Sunni revolt against al-Qaida in Iraq and a cease-fire by radical Shiite cleric Muqtada al-Sadr's Mahdi Army militia.
The U.S. military has said attacks have fallen by about 60 percent since last February.
McCain, the senior Republican on the Senate Armed Services Committee, was accompanied by Sens. Joe Lieberman, an independent, and Republican Lindsey Graham, two top supporters of his presidential ambitions. The weeklong trip will take McCain to Israel, Britain and France.
Police said they found the bodies of three members of a U.S.-allied group fighting al-Qaida in Udaim, 70 miles north of Baghdad. Members of the mostly Sunni groups have been increasingly targeted by suspected al-Qaida members seeking to derail the recent security gains.
A bomb in a parked car in Baghdad's central Karradah neighborhood killed three civilian bystanders and wounded nine, police said, while a separate roadside bomb in eastern Baghdad killed one and wounded three others.