You won't need a PlayStation Plus subscription to play No Man's Sky online, a Sony representative told Game Informer.
The online portion of the game mainly comes to register planets and alien species that you discovered during your adventures in the universe. Although it's possible that you find other players, taking in consideration the scale of the game, the chances of finding someone are very low.
"PS Plus won't be a requirement to play online, however you will need to connected to the internet for your discoveries to register with the universal atlas," said Sony.
No Man's Sky releases on PS4 and PC on the 9th of August in North America, 10th of August in Europe and 12th of August in UK. Also, feel free to check the recent trailers that focus on the combat and trading aspects of the game.
Source: Game Informer