The 'Sin City' actress - who has daughters Honor, five, and Haven, two, with husband Cash Warren - had no idea who the British group were when she first met them a few years ago, despite them topping the charts around the world.
She said: "I didn't know who they were, but a couple of years ago at the Nickelodeon Kids' Choice Awards they asked me to take a picture with them.
"They were these cute young boys with fashiony hair cuts. I was like, 'Oh my God, are you guys in a band?' They looked at me like I was an alien!
"I was the only person on the planet who didn't know who they were. I was talking to Snoop Dogg at the time, so we were like old fogies compared to these guys."
The 'Escape From Planet Earth' star admits her daughters are not fans of the band yet but thinks it is only a matter of time.
Asked if Honor likes One Direction, she said: "Not really, not yet. I'm sure it's coming."
Alba is unsure if she and Cash will ever have any more children, but insists they definitely won't be in the near future.
Discussing if she wants more children, she told Britain's OK! magazine: "I don't know, I'm 32 so I don't know if the shop is closed. I'm sure I won't be trying any time soon."
