U.S. District Judge Amy Berman Jackson said Stone would need to show cause at a hearing on Thursday as to why the posts did not violate a gag order in the case or the conditions of his release.
Stone, who is free on a $250,000 bond and is free to travel to certain U.S. cities without the court's permission, has pleaded not guilty to charges of making false statements to Congress, obstruction and witness tampering as part of Special Counsel Robert Mueller's investigation of Russian meddling in the 2016 election.
Stone's attorneys filed a formal apology with the court on Monday, after he posted a photograph on Instagram of Jackson alongside what appeared to be the crosshairs of a gun.
He later deleted the image and reposted it without the crosshairs before removing it again, according to other media outlets.
Next to the close-up image of Jackson's face, Stone said Jackson was an "Obama appointed Judge who dismissed the Benghazi charges" against Hillary Clinton. He also accused Mueller of being a "Deep State hitman."