Manning would be challenging Democrat Benjamin L. Cardin, who is in his second term in the Senate and is up for reelection in November. Cardin is Maryland's senior senator and is considered an overwhelming favorite to win a third term.
Manning declined to speak about her filing or to say why she might be running when reached at her home in Bethesda on Saturday.
She said she might release a statement in the coming days.
"Our only statement on the record is 'No statement,' " Manning said.
Manning, 30, was convicted in 2013 of the largest leak of classified documents in U.S. history and was sentenced to 35 years in prison. Last year, as President Barack Obama was nearing the end of his term in office, he commuted Manning's sentence to time served, and she was released from a military prison in Kansas.
The news of Manning's filing caught Maryland's political class by surprise Saturday afternoon. It was first reported in a tweet by the conservative media outlet Red Maryland.
Cardin, the ranking Democrat on the Senate Foreign Relations Committee, has an extensive fundraising base in Maryland and is not considered particularly vulnerable to a challenge from any known figures within the state. However, a candidate with national name recognition, such as Manning, who comes in from the outside could tap a network of donors interested in elevating a progressive agenda.
Without mentioning Manning, Sue Walitsky, Cardin's spokeswoman, said: "Senator Cardin is looking forward to a vigorous debate of the issues and a robust conversation with Maryland voters."
Manning would also have to file with the Maryland State Board of Elections to get her name on the ballot.
Manning moved to Maryland after her release from prison. Since then, she has written for the Guardian and Medium on issues of transparency, free speech and civil liberties, transgender rights and computer security, according to her website.
Manning's statement of candidacy was filed with the Federal Election Commission on Thursday.
She is running as a Democrat and refers to Maryland as her "home state" on her website. The Democratic primary is scheduled for the end of June.
Manning's first column for the Guardian said Obama's election in 2008 was a political awakening for her.
Manning wrote that Obama left behind "hints of a progressive legacy" but very few permanent accomplishments.
"This vulnerable legacy should remind us that what we really need is a strong and unapologetic progressive to lead us," Manning wrote. "What we need as well is a relentless grassroots movement to hold that leadership accountable."
Evan Greer, campaign director of the nonprofit organization Fight for the Future and a close supporter of Manning's while she was imprisoned, said the news is exciting.
"Chelsea Manning has fought for freedom and sacrificed for it in ways that few others have," Greer wrote in an email. "The world is a better place with her as a free woman, and this latest news makes it clear she is only beginning to make her mark on it."
Todd Eberly, a political-science professor at St. Mary's College in Maryland, said Donald Trump's unexpected rise to the presidency opened the door for political neophytes such as Manning.
"My initial thought quite literally was, 'Donald Trump is president, Oprah Winfrey is the leading contender for Democrats in 2020, why the hell not Chelsea Manning in the U.S. Senate?' " he said.
Judging from her past statements, Manning's brand could be one of "unapologetic progressivism, no compromise, take no prisoners," he said.
Manning enlisted in the military in 2007 and was deployed to Iraq two years later as an intelligence analyst, according to her website.
In 2010, Manning was arrested after she provided a trove of nearly 750,000 documents to WikiLeaks that included information about the U.S. war efforts in Iraq and Afghanistan, State Department cables and information about prisoners in Guantanamo Bay.
Manning's high-profile leak drew media coverage around the world. U.S. officials said the material placed the lives of U.S. soldiers and Afghan informants at risk, but Manning said she had a duty to inform the public about how the United States was conducting its wars.
Three years later, Manning was convicted on multiple charges, including violating the Espionage Act, and received a lengthy sentence. While serving time at Fort Leavenworth, Manning attempted suicide and went on a hunger strike, before the Army approved her for gender reassignment surgery.
Her case remains politically divisive. She has been lauded as a hero by some on the left but also decried as a traitor by many, including President Trump.
Her felony convictions do not appear to bar her from running for the Senate. The Constitution simply requires that a senator be at least 30 years old, have been a citizen of the United States for nine years and be a resident of the state from which the person is seeking office.
Katherine Shaver contributed to this report.