The producers of Star Trek New Voyages: Phase II, a popular web series starring amateur actors who recreate the series, gained Mr Spinrad's approval to air the script.
But now CBS has sent James Cawley, an executive on the show who also plays Captain Kirk, and Mr Spinrad a "cease and desist" message asserting their copyright.
CBS usually allows fans to indulge their online hobby. In a statement, however, the network said it was "considering opportunities to offer licensed copies of the work." The statement went on: "We fully appreciate and respect the passion and creativity of the 'Star Trek' fan and creative communities.
"This is simply a case of protecting our copyrighted material and the situation has been amicably resolved."
Mr Cawley agreed to cancel production and Mr Spinraid has removed copies of the script from sale on the internet.
David Gerrold, another Star Trek scriptwriter, who works with Phase II, suggested CBS was being heavy handed.
He said: "Star Trek fans are not a sleeping dragon that you want to poke."