The union described News Corp's proposal that Sky News be spun off under an independent company as a "whitewash" and criticised Hunt's acceptance of the plans.
The union is calling on supporters to demonstrate outside the DCMS building in London at 5.30pm today.
"This decision is bad news for democracy and media plurality," NUJ general secretary Jeremy Dear (pictured) said in a statement.
"The reverberations will be felt across the entire media and political landscape. Previous undertakings given by Rupert Murdoch have proved toothless and illusory. Today's whitewash will prove no different."
In a statement today, Hunt defended his decision, saying he believed the undertakings offered would ensure that shareholdings in Sky News would remain unchanged and offer it more independence from News Corporation than it currently has.
"Throughout this process I have been very aware of the potential controversy surrounding this merger. Nothing is more precious to me than the free and independent press for which this country is famous the world over.
"In order to reassure the public about the way this decision has been taken I have sought and published independent advice at every step of the way, even when not required to do so by law. And I have followed that independent advice."
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