Chief U.S. District Judge Mark Walker in Tallahassee ruled on Thursday that the threats clearly violated the right to free speech under the First Amendment of the U.S. Constitution.
"To keep it simple for the state of Florida: it's the First Amendment, stupid," the judge wrote in his temporary order.
The ruling came in response to a lawsuit by Floridians Protecting Freedom, the organization backing the proposed amendment.
Voters in Florida will decide in November on an amendment that would enshrine abortion rights in the state's constitution and overturn the state's six-week abortion ban.
"This critical initial victory is a triumph for every Floridian who believes in democracy and the sanctity of the First Amendment," Lauren Brenzel, director of Yes on 4, the campaign for the abortion rights measure, said in a statement.
Julia Friedland, spokesperson for to Florida Governor Ron DeSantis, said in an email that the ads are "unequivocally false and put the lives and health of pregnant women at risk" and that Florida's abortion law "always protects the life of a mother and includes exceptions for victims of rape, incest, and human trafficking."
Florida's Department of Health sent letters earlier this month, shortly after broadcasters began running ads from the pro-amendment campaign telling viewers that Florida's current abortion ban prevents doctors from performing abortions necessary to save the life or health of the mothers.
The department called that claim "categorically false" and said it endangered public health, and that stations continuing to run the ads could face criminal prosecution.
Walker said that the state could not censor speech simply by declaring it false.
"The State can continue to combat what it believes to be 'false advertising' by meeting plaintiff's speech with its own," the judge wrote.
A hearing is set for Oct. 29 to decide whether the order should be extended. The election is on Nov. 5.
Florida's abortion ban, like that of other states, includes an exception for medical emergencies. However, many doctors and patients have said that those exceptions are so unclear that they do not allow doctors to perform medically necessary abortions. Lawsuits on the issue are pending in several states.
Voters have chosen to protect or expand abortion access in all seven statewide ballot measures put to a vote since the U.S. Supreme Court in 2022 eliminated the nationwide right to abortion, including in conservative strongholds such as Ohio, Kentucky and Kansas.