Some of the jurors’ identities have been shared on social media, with suggestions that they be harassed or made “infamous.”

The Fulton County Sheriff’s Office said Thursday that it was investigating online threats against the grand jurors who voted this week to indict former President Donald J. Trump and 18 others, accusing them of conspiring to overturn Georgia’s 2020 election results.

The jurors’ names are listed early in the sprawling 98-page indictment, as required in Georgia, making the state an outlier among federal and state court systems.

Now some of those jurors have had their faces, social media profiles and possible addresses and phone numbers shared on internet sites, in some cases with the suggestion that they should be harassed — though it was unclear on Thursday if anyone had followed up on those suggestions.

The county sheriff’s office said in a statement that it was aware of online threats against grand jurors and was working with other agencies to track down their origin. It did not answer inquiries about whether any jurors had reported harassment.

Other prosecutions of Mr. Trump have also resulted in threats. A Texas woman was charged this month with threatening to kill Tanya S. Chutkan, the judge in Washington who is overseeing the federal election interference case against the former president.