After the 21 days have passed after acquiring the Zika virus, you're virus-free and good to go

The Zika virus lasts a few weeks at most in the body. It does not cause chronic infection. The time might vary according to each particular case, but Zika infections tend to last between 7 and 21 days. 

During these weeks you should be careful not to get bitten by mosquitoes, so as not to spread the disease to those close to you (use repellant and mosquito nets). After the 21 days have passed, you're virus-free and good to go.