Bethesda has confirmed that the introduction of Fallout 4 mods to the PS4 has been delyed. The feature was set to release this week for PS4 owners, but has been delayed for unspecified reasons.
We regret to say that the PS4 Mods Beta for Fallout 4 has been delayed. We will update everyone when we can.
— BethesdaGameStudios (@BethesdaStudios) 29 June 2016
Bethesda has yet to say when it now expects to launch mods on PS4.