Howell ruled after holding a sealed hearing on the issue.
Miller's attorney, Paul Kamenar, said he plans to appeal the order, which was put on hold pending his action.
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Stoneacknowledged that he was likely the unnamed USA official in the indictment, which listed messages exchanged with Guccifer 2.0, the identity United States investigators say was used by Russian hackers.
That former associate, Andrew Miller, is now facing contempt charges.
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Both Miller and Davis have been called to testify in Mueller's investigation in what may be a sign the special counsel is building a case against Stone. Senate Majority Leader Mitch McConnell said he hopes to have President Donald Trump's nominee confirmed to replace retired Justice Anthony Kennedy before the new court session begins October 1.
Stone has not been contacted by the special counsel's office, but he appears to be under investigation as part of the probe into Russian election interference and possible collusion between Trump's team and Russian officials.
Miller's lawyer had sought to quash the subpoena.
In addition to Miller, John Kakanis, described as a personal assistant to Stone, along with social media expert Jason Sullivan, were subpoenaed by the special counsel over the spring. Stone himself is still under scrutiny in the Mueller probe because of his alleged ties to Wikileaks and his apparent, advanced knowledge that they would release the Democratic National Committee's hacked emails in order to hurt Hillary Clinton.
Kamenar also said a prosecutor with powers as broad as Mueller's should be treated like a USA attorney and be subject to Senate confirmation.