The attack on Sunni Muslim politician Muthanna al-Azzawi's office comes days after a bomb killed another candidate in the November 11 elections for the Shiite-majority parliament.
The gunmen fled after the attack in Yusufiyah, 25 kilometres (16 miles) south of the capital, the source told AFP.
Azzawi is a member of the Baghdad provincial council and belongs to the "Azem Alliance", a centrist Sunni coalition led by Muthanna al-Samarrai.
The candidate "firmly condemned the cowardly attack", saying: "These acts will not stop us from continuing to serve our people."
"The attackers will be punished for their actions sooner or later," Azzawi added on his Facebook page.
A bomb killed fellow Baghdad provincial council member and election candidate Safaa al-Mashhadani on Wednesday when it exploded under his car north of the city.
It also wounded three of his bodyguards.
Mashhadani was running with the Sovereignty Alliance, one of Iraq's largest Sunni Muslim coalitions, led by businessman Khamis al-Khanjar and parliament speaker Mahmoud al-Mashhadani.
The coalition condemned the "cowardly crime", calling it "an extension of the approach of exclusion, targeting and treachery pursued by the forces of uncontrolled weapons and terrorism, all of which seek to silence free national voices".
Prime Minister Mohammed Shia al-Sudani ordered an investigation into the attack on Mashhadani and called for the perpetrators' arrests.
The majority of Iraq's 329 lawmakers represent Shiite parties aligned with neighbouring Iran.
The upcoming elections are the sixth since the 2003 US-led invasion of Iraq, which toppled longtime ruler Saddam Hussein.
In Iraq, the role of prime minister traditionally goes to a Shiite and the presidency to a Kurd, while the speaker of parliament is usually Sunni.
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