Critics say authorities have delayed the elections - and are also seeking to derail an opposition push for a referendum to recall President Nicolas Maduro - because they are frightened of letting Venezuelans have their say.
Maduro, who replaced the popular Hugo Chavez in 2013 after his death, has seen his ratings halve to just over 20% amid a deep economic crisis in the OPEC nation.
The 23 state governors' four-year terms were to end in early January, with elections anticipated for December.
But National Election Board head Tibisay Lucena, who the opposition says is close to the government, said they would instead be held toward mid-2017.