If the Shield is listed on the Monster Stat card (the one that slides into the envelope thing), then that monster ALWAYS has that Shield in effect.
Spoiler (click to reveal)
If the Shield is only listed on the monster's ability card (i.e. the card drawn each round from that monster group's ability deck), then that Shield doesn't take effect until that monster's turn comes up. Thus any attacks against that monster prior to their turn coming up are unaffected.
And while I don't know if this situation actually ever occurs in the game, but if a monster has a Shield value on it's stat card AND one on it's ability for the turn, then that monster would have the Stat shield value prior to their turn coming up, and then after their turn, they would have their Stat Shield value PLUS their ability Shield value.