Police and the Indian franchise of the US chain said no-one was hurt in the attack, which came amid unrelenting rage in India over the arrest and subsequent strip-search of Devyani Khobragade for visa fraud and under-payment of her housekeeper.
India has demanded that the charges be dropped against the diplomat and her father threatened to start a fast if US authorities pressed ahead with the case.
US Secretary of State John Kerry expressed regret over the case in a phone call to national security adviser this week, but US prosecutors have defended the investigation against Khobragade and her treatment.
Police in Mumbai said they were stepping up patrolling of major US outlets including McDonald's after workers of the small Republican Party of India attacked the Domino's store. The group sent pictures to media organisations showing a broken glass door.
"The fact is that (the) American authorities have behaved atrociously with an Indian diplomat. And obviously, America has to make good for its actions," said Manish Tiwari, minister for information and broadcasting.
"So therefore, I think it is a legitimate expectation, that if they have erred, and they have erred grievously in this matter, they should come forth and apologise."
Khobragade was arrested last week and released on $250,000 bail after giving up her passport and pleading not guilty to charges of visa fraud and making false statements about how much she paid her housekeeper. She faces a maximum of 15 years in prison if convicted on both counts.
The US Justice Department confirmed that Khobragade was strip-searched after her arrest. A senior Indian government source has said the interrogation also included a cavity search, although U.S. officials have denied this.
"I want these false and fabricated charges to be dropped," said Uttam Khobragade, the diplomat's father, adding that he would go on a hunger strike if his demands aren't met. "That will be my last option."
Protesters also gathered at the US consulate in Hyderabad for a second day on Friday, shouting slogans, local media said.
Furious that one of its foreign service officers had been handcuffed and treated like "a common criminal", police on Tuesday removed security barriers outside the US Embassy in New Delhi and withdrew some privileges from US diplomats.
Politicians, including the leaders of the two main parties, refused to meet a delegation of visiting US lawmakers.
"Because of the election, they will try to outdo each other," said Neerja Chowdhury, a political analyst and a former political editor of leading Indian newspaper.
"They don't want to be seen as weak on the issue when the mood in the country is one of huge anger about this."
Samajwadi Party, that runs Uttar Pradesh, urged Khobragade to stand for parliament, highlighting how public outrage has turned the case into a battleground for votes.
"Whatever happened with her is condemnable," said Azam Khan, the state's urban development minister, according to media reports. "If she returns to India, we are ready to give her a ticket for the 2014 polls."
Breathless and indignant coverage by Indian TV news channels has added to a sense that national pride has been wounded.
There has been little focus, however, on the predicament of the housekeeper, whose lawyer says was denied her wages, underpaid and now feels it would be unsafe to return to India.
"One wonders why there is so much outrage about the alleged treatment of the Indian national accused of perpetrating these acts, but precious little outrage about the alleged treatment of the Indian victim and her spouse," Manhattan US Attorney Preet Bharara said in a statement on Wednesday.
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