So, the clearest answer is probably “maybe.” When it was a flu-like illness confined to some regions in Africa, Zika wasn’t a high priority so research hasn’t been extensive. The risk to pets in areas where the virus is circulating (areas where there are Aedes egpyti and Aedes albopictus mosquitoes) is probably very low. It would be good to look into the risks associated with domestic animals, including their susceptibility to disease and potential roles as reservoirs, but the likelihood that there is a relevant issue with either of these is probably remote.