"I am now in strict isolation, worried that I have risked my wife's health and angry at the selfishness and arrogance of the anti-maskers who put their own contempt and disregard for decency ahead of the health and safety of their colleagues and our staff."
Mr Schneider warned against turning mask-wearing into a political rather than public health issue, adding that it was a gesture of "common courtesy" to put one on.
Two other Democratic representatives who were in the secure room - Pramila Jayapal of Washington state and Bonnie Watson Coleman, a 75-year-old cancer survivor from New Jersey - have also tested positive for the coronavirus.
In a tweet, Ms Jayapal also denounced Republican lawmakers who refused to wear masks.
"Many Republicans still refused to take the bare minimum COVID-19 precaution and simply wear a damn mask in a crowded room during a pandemic — creating a superspreader event on top of a domestic terrorist attack," she said.
"The duration in the room was multiple hours and several Republicans not only cruelly refused to wear a mask but mocked colleagues and staff who offered them one."
Watson Coleman's office said she believes she contracted the virus while being locked down in the Capitol on Wednesday, when Trump supporters stormed the building to disrupt the certification of Democrat Joe Biden's election victory.
A conservative Republican lawmaker who was in the lockdown room, Marjorie Taylor Greene of Georgia, wished Ms Jayapal a full recovery but sought to deflect blame on the Democratic speaker of the House, Nancy Pelosi.
"Before you point fingers at me or anyone else, you need to talk directly to @SpeakerPelosi about exposing ALL of us to COVID when she called back POSITIVE COVID House members last week for votes for Speaker!" Ms Taylor Greene said in a tweet.
The United States is the world's hardest-hit country and more than 376,000 people have died from coronavirus - with about 3,000 more dying every day.