Manning had been working as an intelligence analyst in Iraq.
She came out as transgendered shortly after her sentencing, but the military denied her request for hormone therapy treatment while behind bars.
The Democratic Senate incumbent is Ben Cardin, who was first elected in 2006 and is the senior Democrat on the Senate Foreign Relations Committee.
Ms Manning is a transgender woman, and was known as Bradley Manning at the time of the leaks.
Former President Obama said the sentence she was given was "disproportionate", but President Donald Trump has labelled her an "ungrateful traitor" who "should never have been released from prison".
Manning's lawyers at the American Civil Liberties Union, Nancy Hollander and Vincent Ward, said in a joint statement that "Chelsea has already served the longest sentence of any whistleblower in the history of this country".
Representatives for Cardin did not immediately return calls for comment Saturday.
Manning has now gone from prison to US senatorial candidate in less than a year during which she often made headlines, as the fame and infamy she gained by leaking a trove of classified documents follows her after release.
The conservative media organization Red Maryland first reported Manning's intention to run.
The news of Manning's candidacy provoked a wave of outrage on Twitter.
She has written about transgender rights and bullying in columns published on the website Medium. Paul Sarbanes in 2007, is not considered particularly vulnerable to challenge. When reports broke last week that Immigration and Customs Enforcement agents were raiding 7-11 stores, Manning called the agency "the new Gestapo". Her candidacy would undoubtedly bring attention, both in Maryland and around the nation, to transgender rights and the rise of the security state.
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