One of the drugs is already on the market as a treatment for tapeworm, researchers said.
"We focused on compounds that have the shortest path to clinical use. This is a first step towards a therapeutic that can stop transmission of this disease," said Hengli Tang, a professor at Florida State University (FSU) in the US.
One of the identified compounds is the basis for a drug called Nicolsamide, commonly used to treat tapeworm.
Though the Zika virus was discovered in 1947, there was little known about how it worked and its potential health implications - especially among pregnant women - until an outbreak occurred in South America last year.
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The virus, among other diseases, can cause microcephaly in fetuses leading them to be born with severe birth defects.
Researchers around the world have been working to better understand the disease - which can be transmitted both by mosquito bite and through a sexual partner - and also to develop medical treatments.
They screened 6,000 compounds that were either already approved or were in the process of a clinical trial because they could be made more quickly available to people infected by Zika.
"It takes years if not decades to develop a new drug. In this sort of global health emergency, we do not have time. So instead of using new drugs, we chose to screen existing drugs. In this way, we hope to create a therapy much more quickly," said Hongjun Song from Johns Hopkins University in the US.