The Imperial College London team created a model using data from the current outbreak in Latin America.
But a Zika expert said predicting anything with any degree of certainty was impossible.
The scientists, from the Medical Research Council Centre for Outbreak Analysis and Modelling at Imperial, calculated that the epidemic, which began in Brazil in 2015, would burn itself out within three years.
Because the virus is unable to infect the same person twice, as more and more people become infected, reaching a level called "herd immunity", infection levels fall and the epidemic dies out.
Until there was a new generation who had not been exposed to Zika virus, there would be a long period with few new cases, the researchers said.
They said this mirrored the pattern of other epidemics, such as chikungunia - a virus similar to Zika.
Microcephaly link
Earlier this year, the World Health Organization declared the Zika virus a global public health emergency because of the risk to newborn children.
Although Zika infection is largely mild, with most people having no symptoms, it is known to cause microcephaly - babies born with undersized heads.
In severe cases, children can die and babies who survive can face intellectual disability and developmental delays.
The Olympic Games are going ahead in Rio, Brazil, in August, despite recent concerns from leading scientists that holding the event is "unethical".
The research paper said the current outbreak was not "containable" and targeting the Aedes aegypti mosquito carrying the virus would have limited impact.
Prof Neil Ferguson, lead author of the research, said that any efforts to slow the spread of the virus could actually prolong the current epidemic.
"Slowing transmission between people means the population will take longer to reach the level of herd immunity needed for transmission to stop.
"It might also mean that the window between epidemics could actually get shorter."
More about:
