"The American Center in Kolkata and the Library will remain closed to the public until further notice. Any inconvenience is regretted. Consulate Kolkata services will continue to function during the lapse in Congressional appropriations," the statement said.
The US government has been shut down after a few Republicans joined Democrats in blocking a crucial measure which would have provided short-term funding for the Pentagon and other federal agencies.
"If you have a scheduled visa interview or American Citizen Services appointment, please arrive at the consulate at your designated time," the statement said.
On Saturday, the US government officially shut down for the first time in five years.
In a shutdown, non-essential government employees are furloughed, or placed on temporary unpaid leave. Workers deemed essential, including those dealing with public safety and national security, keep working.
There have been four government shutdowns since 1990. In the last one in 2013, more than 800,000 government workers were put on temporary leave.
"We're just in a holding pattern. We just have to wait and see. It's scary," Noelle Joll, a 50-year-old furloughed US government employee, told AFP in Washington.
As US lawmakers wrangled over government funding, protesters turned out in cities including Los Angeles, New York and Washington to express their opposition to US President Donald Trump, and their support for women's rights.
With inputs from agencies