Police said initial reports showed all three explosions were caused by female suicide bombers.
At least a million people are expected to visit the Kadhamiya shrine in northwestern Baghdad for the event, which peaks on Tuesday. Iraqi security forces have clamped tight security in the area.
All the explosions were close to Baghdad's Karrada district in central Baghdad, an area many pilgrims would pass through on their way to the shrine. It was unclear if the victims were pilgrims.
Gunmen killed seven pilgrims in southern Baghdad on Sunday as they made their way to the shrine on foot.
Sunni Islamist al Qaeda has often targeted Shi'ite pilgrims taking part in religious events in Iraq. The insurgent movement considers Shi'ism heretical.
The pilgrimage this week marks the death of one of Shi'ite Islam's 12 imams.
