Trump's expected appearance before a judge in Manhattan on Tuesday, as the Republican mounts a bid to regain the presidency, could further inflame divisions in the United States.
The specific charges are not yet known, though CNN reported that Trump faced more than 30 counts related to business fraud.
Daniels has said she was paid to keep silent about a sexual encounter she had with Trump in 2006.
Bragg said Congress does not have authority to interfere with a New York legal proceeding and accused the lawmakers of escalating political tensions.
Bragg's office prosecuted Trump's business on tax-fraud charges last year, leading to a $1.61 million criminal penalty, but Trump himself was not charged.