A MOV (metal oxide varistor) fell on hard floor. Could it be damaged?
Probably not, if the coating is not chipped. 

If you read the datasheet you will find a voltage rating at which the current is guaranteed to be less than some nominal value (maybe 1mA). If you (briefly) apply the voltage and the current is less (typically it will be very much less) then the MOV is (most likely) functionally okay. 

If the application requires very high reliability (eg. space or medical equipment) you may wish to discard a 50 cent part rather than bother, or use it for engineering samples and not items to be shipped.