This is a common question and the answer is "yes" with a caveat:

Fla. Stat s.718.110(3) says that "[a]ny amendment restricting unit owners' rights relating to the rental of units applies only to unit owners who consent to the amendment and unit owners who purchase their units after the effective date of that amendment." This statute effectively "grandfathers in" all existing owners when creating new rental restrictions except for the owners who choose to restrict themselves by voting for the amendment.

The Declaration can be amended to restrict leasing with, of course, the one caveat that only unit owners that actually consent to the amendment will be affected by such an amendment. Making this amendment would require compliance with the amendment process set forth in the Declaration.