Writing in the journal Science, they said this could lead to a gap of 10 years before the next epidemic.
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.
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."
However, Prof Ferguson said there were still many unanswered questions about Zika which could affect predictions.
The virus could become endemic in Latin America which would result in smaller, frequent outbreaks, for example, and he said no-one yet understood why Latin America was particularly affected.
"One possibility is climate may have in some way aided spread of the virus, as spread coincided with an El Nino event," he said.
"Genetic mutation of the virus might also have played a role, although early data currently give limited support for this hypothesis."
He added that previous exposure to Dengue fever might heighten the Zika infection in a person, as recent studies had suggested.
But Jonathan Ball, professor of molecular virology at the University of Nottingham, said although the paper was interesting, there were still a lot of gaps in the data.
"In truth, there are so many really important scientific unknowns surrounding Zika that it is impossible to predict what will happen with any degree of certainty.
"Key questions that remain unanswered include how many people have been infected, the duration that people are immune to the virus once they have been infected, whether or not past exposure to related viruses like Dengue affects Zika susceptibility and if wildlife reservoirs of virus now exist."
He added: "These will only be answered with improved diagnostic tests and further research in the laboratory and out in the field."
The current Zika epidemic is likely to end within three years because there will be too few people left to infect, a team of scientists is predicting.