The shutdown began at 12:01 am (local time) after a few Republicans joined Democrats in blocking the crucial measure would have provided short-term funding for the Pentagon and other federal agencies.
Trump blamed the Democrats for the shutdown which comes exactly a year after he was sworn in as the 45th President of the United States.
"Dems want a shutdown in order to help diminish the great success of the tax cuts, and what they are doing for our booming economy," he said.
The short-term spending bill was passed by the House on Thursday.
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This is part of the Democrats strategy to force President Trump and the Republicans to negotiate with them on illegal immigrants who are facing deportation.
The effect of the shutdown would be felt most from Monday when the federal government employees would not be able to join for their work and be forced to stay at home without pay.
The last time that a government shutdown happened was in 2013.
Earlier in the day, the Office of Management of Budget said it was preparing for "what we're calling the Schumer Shutdown".
The Director of Office of Management of Budget Mick Mulvaney told reporters that efforts were being made to have the government shutdown less impactful than it was in 2013.
"We're going to manage the shutdown differently. We are not going to weaponize it. We're not going to try and hurt people, especially people having to work for this federal government. But we still need Congress to appropriate the funds," he said.
Fanny and Freddy will be open, the post office will be open, the TSA will be open, but again all of these people will be working for nothing, which is simply not fair, he said.
US Postal Services would be working.
The last government shutdown lasted for 16 days in October 2013. The previous shutdown before that was for 21 days that ended on January 6, 1996.
"This is completely unfair and uncompassionate for my Democratic colleagues to filibuster government funding, harm our troops, and jeopardise health coverage for nine million children because extreme elements of their base want illegal immigration to crowd out every other priority," Senate Majority Leader Mitch McConnell said.
He argued that immigration reform needed to be handled separately from the spending bill.
Trump has cancelled his scheduled weekend trip to Mar-a- Lago in Florida. However, he would continue with his trip to Davos to attend the World Economic Forum meeting next week.
Democratic Senator Chuck Schumer is the Senate Minority Leader.
"Senate Democrats own the Schumer Shutdown. Tonight, they put politics above our national security, military families, vulnerable children, and our country's ability to serve all Americans," Sanders said.
"We will not negotiate the status of unlawful immigrants while Democrats hold our lawful citizens hostage over their reckless demands. This is the behaviour of obstructionist losers, not legislators," Sanders said in a statement.
Earlier, Trump held a last-minute meeting with Schumer to avert a government shutdown.
"We had a long and detailed meeting. We discussed all of the major outstanding issues, we made some progress, but we still have a good number of disagreements. The discussions will continue," Schumer said soon after his meeting with Trump.