WASHINGTON — As Hillary Clinton moves toward the Democratic presidential nomination, she faces legal hurdles from her use of a private computer server as secretary of state that could jar her campaign’s momentum in the months ahead.

Foremost among a half-dozen inquiries and legal proceedings into whether classified information was sent through Mrs. Clinton’s server is an investigation by the F.B.I., whose agents, according to one law enforcement official, could seek to question Mrs. Clinton’s closest aides and possibly the candidate herself within weeks.

It is commonplace for the F.B.I. to try to interview key figures before closing an investigation, and doing so is not an indication the bureau thinks a person broke the law. Although defense lawyers often discourage their clients from giving such interviews, Democrats fear the refusal of Mrs. Clinton or her top aides to cooperate would be ready ammunition for Donald J. Trump, the Republican front-runner.

A federal law enforcement official said that barring any unforeseen changes, the F.B.I. investigation could conclude by early May. Then the Justice Department will decide whether to file criminal charges and, if so, against whom.