The incident is the latest in a series of attacks targeting Western-linked brands in Iraq that started last week.
A group of "30 men attacked" a branch of the US fast-food chain KFC and a Chilli House restaurant in Palestine Street, a security source said.
Security forces fired shots in the air to disperse the group before arresting at least two people, the official added.
The attack caused material damage but no injuries, a security source said.
Local media shared videos showing masked men smashing glass and furniture at the KFC branch.
In response, security forces have increased their deployment in neighbourhoods where US brands are located.
Early Thursday, two stun bombs exploded in front of a dealership of the US construction equipment company Caterpillar and the Cambridge Institute, which a resident identified as a likely Iraqi-owned language learning centre.
On May 26, a makeshift bomb was thrown at a KFC branch, causing minor damage. The next night, masked men broke into another branch, smashing glass.
The US ambassador to Iraq, Alina Romanowski, denounced Thursday several "attacks against US and international businesses" in Baghdad.
Iraq does not recognise Israel's statehood, and all of its political parties support the Palestinian cause.
Shortly before Monday's attack, Iraq's powerful pro-Iran Kataeb Hezbollah called to "boycott and expel" what they denounced as "spy" entities affiliated with "the occupation".
The group, which Washington considers a "terrorist" organisation, has repeatedly called for US troops to withdraw from Iraq.
Last month, influential Iraqi cleric Moqtada Sadr renewed his calls to close the US embassy in Baghdad "through diplomatic means without bloodshed", after an Israeli strike killed dozens of civilians in a camp in Gaza.
Since the war in Gaza started in October, a boycott movement spearheaded by pro-Palestinian activists has targeted major Western brands, such as Starbucks and McDonald's.
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