The bombs struck as the pilgrims traveled to Karbala to mark Arbaeen, the end of the 40-day mourning period for the Shiite religious figure Imam Hussein, the Los Angeles Times reported.
One bomb detonated in a car parked south of the city, killing at least eight people and wounding 35, security and medical officials said. The second car bomb exploded east of the city, killing at least 14 dead and wounding 40 others.
Mohammed Tnayish told the Times he was walking with his wife when the second blast occurred.
"Many charred bodies were there -- women, children and men. It was so sad and horrible. Blood was everywhere," Tnayish said. "It's so frustrating to have car bombs every few days against Imam Hussein pilgrims. Where are the security forces? They should have better measures and intelligence to prevent such terrorist acts."
Al-Sumaria reported Maj. Gen. Thamer Saleh Hasan was killed in a bombing as he was leaving his home in western Baghdad Monday.
Also Monday, the governor of Iraq's Salaheddin province, Ahmed Abdullah, was unharmed after his convoy hit a roadside bomb in central Tikrit, CNN said. Tikrit police said five of his guards were wounded.