"Surprisingly" refers to the statement or event that caused a surprise. "Surprisingly, far more Spaniards have high-speed Internet connections than Americans." (I don't know if that's true, but if it is, it might surprise some people to hear it.)
"Surprisedly" describes a person's reaction to a statement or event. " 'I didn't expect you until tomorrow,' said Tom surprisedly as he hurried to straighten out the mess on his desk."