From my experience, I would recommend immediately contacting the credit card issuer (or bank for a debit card) and having the card deactivated (as the number is potentially compromised) and having a new one sent to you. For situations where you need a card right away, most banks will allow you to go to the branch and get a temporary ATM-only card.
It will still be difficult for thieves to use the card as they will be missing the CID (card security code) that is on the back of the card, but it's still not impossible.