Mosquito bites have a host of potential issues. If there is no chance I will become pregnant, should the potential for zika cause me anymore concern about mosquito bites then all of the other things they can carry?
For adults, Zika virus is like flu. Apart from fever and maybe nausea, you shouldn't have to worry.
Edit: since it seems sources are of bad need, here is one confirmation from a very recent study (Petersen 2016).