Harry Reid accused FBI director James Comey of violating an act which bars officials from influencing an election.
News of the FBI inquiry comes less than two weeks before the US election.
The bureau has meanwhile obtained a warrant to search a cache of emails belonging to a top Clinton aide.
Emails from Huma Abedin are believed to have been found on the laptop of her estranged husband, former congressman Anthony Weiner.
There are reportedly 650,000 emails to search through on the laptop, making it unlikely investigators can give a verdict on them before election day.
Mr Reid also accused Mr Comey of withholding “explosive information about close ties between [Republican candidate] Donald Trump, his top advisers, and the Russian government”.
“The public has a right to know about this information. I wrote to you months ago calling for this information to be released to the public,” Mr Reid said.
The FBI believes the emails might be “pertinent” to its previous inquiry into Mrs Clinton’s use of a private server when she was secretary of state in the Obama administration.
The case was closed in July without any charges being brought against Mrs Clinton.
Mr Weiner is subject to a separate investigation on suspicion of sending sexually explicit messages to an underage girl.
In a letter, Mr Reid accused Mr Comey of practising double standards with the intention of helping one political party over another.
He said Mr Comey may have violated the Hatch Act, which bars officials from using their position to influence an election.
“Through your partisan actions, you may have broken the law,” he said.
Richard Painter, a professor at the University of Minnesota Law School and the chief White House ethics lawyer from 2005 to 2007, revealed on Sunday he had filed a complaint against the FBI with the Office of Special Counsel, which investigates Hatch Act violations.
Writing in the New York Times he said: “I never thought that the FBI could be dragged into a political circus surrounding one of its investigations. Until this week.”
What is the Hatch Act?
The act, passed in 1939, prevents federal employees from using their positions to benefit a particular political party. It also applies to some state, Washington DC and local government employees.