US-led forces in Iraq have vowed to kill or capture al-Sadr and destroy his Mahdi Army militia.
Witnesses said US forces withdrew from the city, 110km southwest of Baghdad, after the incursion early on Friday. Hospital sources said 15 other Iraqis were wounded in the clashes.
The clashes took place in al-Saadia neighbourhood near al-Mukhayyam mosque in Karbala, Aljazeera's correspondent in Iraq reported.
Other clashes also erupted in al-Shaabiya, al-Talib, and al-Jamiya neighbourhoods, the correspondent added.
On Thursday US tanks swept into Najaf - another Shia holy city - and Karbala, pounding and killing fighters loyal to
Meanwhile, a roadside bomb killed four Iraqi policemen and wounded one in the northern Iraq city of Mosul, Aljazeera's correspondent reported.
The bomb detonated as a patrol was passing through the al-Jadida district in the southern part of the city. Police said there was an exchange of gunfire with the attackers immediately after the attack, but no one was arrested.
Mosul, about 400km north of Baghdad, has been relatively quiet in recent weeks, as fighters have focused attacks in and around Falluja, west of Baghdad, and in cities to the south of the country.
Meanwhile, Tikrit's chief of police said the US had released 33 Iraqi prisoners from its military bases in the area. He said 13 detainees were handed over to local police for interrogation.