Sorry for the belated response, traveling last week.
If your policy has Business Income (aka Loss of Income or Business Interruption) you may have coverage. Please note that there is a waiting period (24-72 hours is typical) for which you would not be compensated. Depending upon the nature of the event, Equipment Breakdown coverage may also come into play.
On a related note, Cyber Liability policies can protect an insured from the costs associated with data breaches.