Her lawsuit also targets Mr Cheney's former aide Lewis Libby and former top presidential advisor Karl Rove, saying they tried to destroy her career.
Ms Plame and her husband, former US diplomat Joseph Wilson, claim the men violated the couple's rights when they conspired to leak her work as a Central Intelligence Agency undercover operative to the press in order to strike out at Mr Wilson for clashing with the Bush administration over the Iraq war.
"Those officials sought to punish Mr. Wilson for his public statements regarding assertions by the president of the United States in the 2003 State of the Union address that he used to justify war against Iraq," said the lawsuit, which lists 10 other unnamed defendants as "John Does".
"As their chief method of punishment, the White House officials destroyed Mrs Wilson's cover by revealing her classified employment with the CIA to reporters."
The two said they had suffered "gross invasions of privacy" as a result of the White House actions, which also caused them to "fear for their safety and the safety of their children".
The exposure also impaired Ms Plame's ability to perform her CIA job and pursue her career, the charges alleged.
Ms Plame has since quit the spy agency.
The couple is seeking an unspecified level of compensatory and punitive damages from the defendants in the suit.
A spokesman for Mr Rove said the allegations are without merit.
It was revealed last month that Mr Rove would not be charged over the leak.
Mr Libby has been charged with perjury and obstructing justice in connection with the leak.
He denies the charges, has however resigned pending trial.
A spokeswoman for Mr Cheney said he would make no comment as the matter is before the courts.
Retaliation
The case grew out of Mr Wilson's allegations following the March 2003 invasion of Iraq that Mr Bush and others had falsely claimed that Iraq had sought uranium in Niger for weapons programs, published in The New York Times.
In June 2003 conservative columnist Robert Novak cited unnamed senior administration sources when he revealed in a column criticising Mr Wilson that his wife was a CIA operative.
A special federal prosecutor, Patrick Fitzgerald was then named to lead an investigation into the outing of Ms Plame's identity, which could carries felony charges.
Fitzgerald interviewed several journalists who admitted having spoken to top White House officials about Ms Plame during the period.
On Wednesday, Mr Novak revealed in a column that two of his sources on Ms Plame were Mr Rove and CIA public information officer Bill Harlow.
He said a third source had not authorised him to reveal the source's name.