You cannot remove a fake review immediately as it needs to be reported to Facebook to be reviewed. Once you have reported the review and if Facebook finds that the review is fraudulent or it does not comply with its guidelines it will be removed from your business page.
In this current day and age, the power of a review is unmeasurable. It is normal to have a negative review every once in a while, as most clients become suspicious if a business only has five-star reviews. Not only have online reviews become the new word of mouth, but it has also become the Achilles heel for some businesses when a fake review was left by a competitor or a disgruntled client.
It is important to show customers that you take negative reviews seriously, so while you wait for a reply from Facebook it might be a good idea to respond to the fake review in the meantime. If you don't know what to reply here is a good example:
"Thank you for your review. While we take customer satisfaction very seriously we believe that your review might have been made in error as we have no record associated with your details. Please contact us at _______ in order for us to attend to your complaint in a proper fashion."
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