Sanders tweeted that the White House would "never tolerate a reporter placing his hands on a young woman just trying to do her job".
"As a result of today's incident, the White House is suspending the hard pass of the reporter involved until further notice."
Costa was called a "rude, terrible person" by Trump at the press conference when he questioned the president.
A staff member tried to take away his microphone during the back and forth.
They began sparring after Acosta asked Trump about the caravan of migrants heading from Latin America to the southern US border. When Acosta tried to follow up with another question, Trump said, "That's enough!" and a White House aide unsuccessfully tried to grab the microphone from Acosta.
Trump accused a PBS reporter of posing a racist question when she asked him about white nationalists.
"It's such a hostile media," Trump said during his post-Midterms news conference, after ordering reporter April Ryan of the American Urban Radio Networks to sit down when she tried to ask him a question.
The president complained that the media did not cover the humming economy and was responsible for much of the country's divided politics. He said that "I can do something fantastic, and they make it look not good."
- Additional reporting AP
