The bomb went off near the entrance of the Sacred Heart church, which is surrounded by concrete blast walls, near Tahriart Square in central Baghdad.
Two passing civilians and two policemen were wounded, an interior ministry official and doctor at Ibn Nafis hospital said.
The church was empty at the time as Easter services were held earlier in the day, the building's security guards said.
Security officers at the site barred reporters from entering the church, but confirmed the casualty toll.
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A pick-up truck belonging to federal police and a civilian saloon car were badly damaged by the blast.
Shards of glass were also scattered across the road in front of the church, which was briefly closed off as forensics teams analysed the scene and the damaged vehicles were towed away.
The number of Iraqi Christians has dwindled from an estimated between 800,000 and 1.2 million prior to the 2003 US-led invasion that ousted Saddam Hussein to about 400,000 today.
Most of them live in Baghdad, the area surrounding the northern city of Mosul and parts of the autonomous Kurdistan region in the north of Iraq.
In other violence in Iraq, army General Abdulghani Mohammed was injured by a magnetic "sticky bomb" attached to a military vehicle in the Al-Amriyah neighbourhood in the west of the capital, the interior ministry official said.
A roadside bomb also exploded near the Iranian embassy in the centre of the capital, but no casualties were reported.
And in the northern ethnically divided city of Kirkuk, an Iraqi army captain was killed by a "sticky bomb" early on Sunday morning, local police said.
The latest violence comes with just months to go before a year-end deadline for the fewer than 50,000 US troops currently in the country to withdraw, under the terms of a bilateral security pact.
Violence has dropped off dramatically across Iraq since its peak in 2006 and 2007, when tens of thousands were killed in nationwide sectarian bloodshed. But attacks remain common, especially in the capital.
A total of 247 people were killed in violence in Iraq in March, according to official figures.
