The bomber was a woman, a local police officer said on condition of anonymity.
Salim Kadhim, spokesman for the Karbala health directorate, said seven Iranian pilgrims were among the wounded.
Police imposed an indefinite curfew in the central districts of the city shortly after the blast.
No group has yet claimed responsibility for the attack, but the US military has said that al-Qaeda, a Sunni Muslim organisation, has sought to step up attacks on Shia Muslims.
Iraq has been hit by several suicide bombings in recent months, with women launching some of the attacks.
Rear Admiral Gregory Smith, a US military spokesman, said on Sunday: "Late in 2007 there were about eight or 10 [suicide bombings] a month; in the month of February, there were 18. There is an increase."