A 32-year-old Indian national is being investigated for participating in a public assembly without a police permit, the police said on Wednesday.
He had allegedly committed the offence at Marina Bay to protest against India's Citizenship (Amendment) Act.
The Straits Times understands that the man had posted a picture of himself on social media holding a placard to express his unhappiness. His occupation and residence status in Singapore are currently unclear.
It is believed more than one person could be investigated in the case.
In a statement, the police said that organising or participating in a public assembly without a police permit is illegal and an offence under the Public Order Act.
Besides groups of demonstrators, the Act also applies to individual demonstrations in support of or against views or actions, publicising a cause or commemorating an event.
Last month, the police impounded the passport of a Hong Konger, restaurant owner Alex Yeung, while he was under investigation for allegedly organising a gathering in Singapore for people to air their views on the Hong Kong protests.
In March, the police said they were investigating civil rights activist Jolovan Wham for protesting outside the State Courts without a valid permit in December last year.
"The police will not grant any permit for assemblies that advocate political causes of other countries. Foreigners visiting or living in Singapore should abide by our laws," the statement said.
Street protests have erupted across India since the Citizenship (Amendment) Act was passed last week. The change, which some say threatens to erode India's secular foundation, seeks to provide citizenship to non-Muslim illegal immigrants from Afghanistan, Pakistan and Bangladesh.
The United Nations human rights office has called the law "fundamentally discriminatory".