Thousands of babies in South America have been born with underdeveloped brains since the outbreak of the virus
Researchers have discovered how the Zika virus causes microcephaly - a condition that stunts head and brain development.
Tiny brains - no larger than a pinhead - were created using 3D printers and infected with the disease by scientists at Johns Hopkins University in Baltimore, US.
The study - published in the journal Cell - showed that Zika caused the brains of unborn babies to shrink by attacking cells responsible for brain growth and turning them into "virus factories".
The disease restricted the growth of the cortex, the outer layer of the brain which helps a person's perception, attention, memory and consciousness.
Guo-li Ming, professor of neurology, neuroscience, and psychiatry and behavioural sciences at the university, said: "If infection occurred very early in development, the virus mostly infected the mini-brains' neural progenitor cells, and the effects were very severe.
"After a while, the mini-brains would stop growing and disintegrate.
"At a later stage, mimicking the second trimester, Zika still preferentially infected neural progenitor cells, but it also affected some neurons.
"Growth was slower, and the cortex was thinner than in non-infected brains."
Her husband and research partner Hongjun Song, professor of neurology and neuroscience at Johns Hopkins, said the research team, which included members of other US universities, would publish the 3D printing files.
This would allow other researchers to make the bioreactors needed to grow the mini brains.
He said the technology could also be used to grow so-called dopaminergic neurons to replace those that die off in patients with Parkinson's disease.
"This is the next frontier of stem cell biology," he said.
Thousands of babies in South America have been born with underdeveloped brains since the outbreak of the virus last year.
The World Health Organisation has declared Zika to be a global public health emergency.
Scientists are still searching for a vaccine for the virus, which has no known cure.