Democrats have said that could encourage Trump supporters to harass minority voters and have launched a legal blitz in six states to prevent that from happening.
Numerous studies have found that U.S. voter fraud is exceedingly rare.
The ruling does not prevent the state Republican Party from sending trained volunteers into polling places to make sure election laws are being followed.
However, it does apply to Trump supporters who may take it on themselves to monitor voting activity independent of the party. It prevents them from verbally harassing voters near polling stations, or taking pictures of them.
The ruling also applies to groups supporting Clinton's presidential bid.
It also shuts down an exit poll organized by Trump ally Roger Stone, who said he aims to uncover examples of vote manipulation. Stone told Reuters on Monday that participants are trained not to harass voters. Some 118 people in Ohio have signed up to participate through a web site called Stop the Steal. Stone did not immediately respond to a request for comment.
Ohio Republicans and the Trump campaign did not immediately respond to requests for comment.