Foreigners visiting or living in Singapore have to abide by its laws and should not import the politics of their home country here, police said in a statement on Thursday.
Those who break the law will be dealt with firmly, and it may result in individuals having their visas or work passes terminated, they said.
The statement comes amid plans to hold a Jallikattu-related event at Speakers' Corner in Hong Lim Park, as well as in other locations in Singapore.
Police came to know of these plans and reminded members of the public that organising or participating in a public assembly without a police permit is illegal.
The planned gatherings come as protests in parts of India, including in Tamil Nadu and Delhi in recent days, gathered strength as supporters of Jallikattu - a controversial bull-taming festival - rallied to demand that the Indian government lift a ban on the traditional event.
A notice calling on Tamils in Singapore to gather at Sembawang Park at 6.30pm today to show solidarity with pro-Jallikattu protesters in India has been circulating online.
Police added that only Singapore citizens and permanent residents are allowed to take part in assemblies held without a police permit at Speakers' Corner, subject to the rules of the designated free-speech area.
"Organisers of such events have a responsibility to take appropriate measures to ensure that our laws are complied with," the police said.
Jallikattu, a traditional bull-taming sport, is typically practised in Tamil Nadu as part of Pongal celebrations in January, and is viewed as a cultural symbol.
India's Supreme Court outlawed Jallikattu last year after a plea by animal-rights groups, which have long argued that the event is cruel.
The bulls are let loose into an open field and young men compete to subdue them bare-handed, meaning that participants, spectators and the bulls often get wounded or even killed.
But demonstrators have taken to the streets in India to demand that the ban be lifted, arguing that they are supporting the preservation of their culture.