The attacks against the pilgrims appear to be part an extremist campaign to rekindle the sectarian conflict that nearly pushed the country into full-scale civil war two years ago.
A suicide bomber on Thursday detonated an explosive belt packed with nails among Shia worshippers in Karbala near the Imam Hussein shrine, killing eight pilgrims and wounding more than 50 more.
At least 12 people were killed and more than 40 others wounded in bombings in Baghdad the previous day.
The attacks also targeted Shia pilgrims travelling to Karbala.
About 40,000 Iraqi troops have been deployed along major routes to Karbala.
Officials say security cameras have been installed near the Imam Hussein shrine to keep a lookout for possible threats.
The pilgrims will be celebrating Monday's end of 40 days of mourning that follow Ashura, the anniversary of the seventh-century death of the Prophet Muhammad's grandson Hussein.