'Of course I do.'
'Well, while you and your husband were sleeping, three fairies came in and said the wizard had placed three curses on his daughter: to come upon three horses and leap on the white horse, which would be her undoing. But, they added, should somebody quickly cut off the horse's head, nothing would happen. And whoever breathed a word of this would turn to stone.'
As he said those words, poor Peel's feet and legs turned to marble.
The young woman understood. 'That's enough, please!' she screamed. 'Don't tell me any more!'
But he went on: 'Doomed whether I speak or keep silent, I choose to speak.'
- Italo Calvino, Italian Folktales, 'Pome and Peel'
The exact nature of the curse doesn't matter, as long as it's suitably terrible - it doesn't even have to be death or petrification, perhaps just the loss of items or something else valuable will be enough to motivate the player. So, the player hears something or reads something with a curse on it (make sure it's something they actually seek out for themselves, not just foisted upon them at random). At the time you say "No, there's nothing interesting about it." After the session, you secretly tell the player what they've learned and what the dire consequences are if they repeat it to anyone else.
Now, the player can still act upon what they've learned i.e. cut off the horse's head. But when questioned about it, they can't really say anything except "I can't tell you." (For extra cruelty, you could make it that even saying that you can't say will trigger the curse - so the player has to explain their actions with "I just felt like it," or some other improbable reason). Unless your players are slow-witted or really into PvP, they'll probably catch on to what's happening pretty quickly, but the tension it creates will still be fun.
Alternate, less devious option: the entire party hears about the curse, but they can't repeat a word of it to any NPCs. Insert your own hijinks here.