Populations in India, Indonesia and Nigeria are some of the most vulnerable to transmission, the researchers said.
They used data on air traveller numbers to help model their predictions.
However, they acknowledge that immunity to the virus could already exist in some areas and could reduce the risk.
The research team, from the London School of Hygiene and Tropical Medicine, Oxford University and the University of Toronto, Canada, said "vast numbers" of people were living in environments where it would be hard to prevent, detect and respond to the virus.
They looked at factors such as the numbers of people who travelled from Zika-affected areas in South America to Africa and Asia, the presence of mosquitoes that can pass on the virus, and the climate in the regions to assess which countries could be most at risk from an outbreak.
In their study, the researchers suggest that the Philippines, Vietnam, Pakistan and Bangladesh could be particularly vulnerable to a Zika outbreak because of their limited health resources.
Dr Kamran Khan, study author from St Michael's Hospital in Toronto, said: "The impact on populations will also depend heavily on the country's ability to diagnose and respond to a possible outbreak."
And he added: "Our findings could offer valuable information to support time-sensitive public health decision-making at local, national, and international levels."
More than 65 countries and territories now have continuing Zika transmission.
The infection, spread by mosquito bites, reached Africa recently.
In Brazil in 2015, Zika virus was linked to an unprecedented rise in the number of children being born with unusually small heads, called microcephaly.
But the researchers said there were still many unknowns about the virus and how it spreads, including which species of mosquito transmits the virus and whether some populations are immune to the virus because of previous outbreaks in the area.
Zika experts say the risk of the virus spreading is at its highest over the summer months when people are travelling between America and other parts of the world.
Warm temperatures during the summer also mean the mosquitoes which transmit the virus can survive longer.
Dr Oliver Brady, co-study author and research fellow in mathematical modelling at the London School of Hygiene & Tropical Medicine, said: "Countries such as India, Indonesia and Nigeria are predicted to be at highest risk of Zika introduction with up to 5,000 passengers a month arriving from Zika endemic areas.
"Should Zika be imported into these areas the impact on their health systems could be very severe."
Jonathan Ball, professor of molecular virology at the University of Nottingham, said it was evident that travel and trade would help spread the Zika virus around the world.
He added: "While this study reminds us that many parts of the world have ideal conditions for the virus to take hold it can't pinpoint exactly where this will happen.
"This is a virus that has circulated for years in parts of Africa and Asia and so, many of these people may already have been exposed and have protective immunity."
He said the only way of finding out which countries would be affected in future was "by doing science on the ground".
This entails finding out the numbers of people that are susceptible to infection and also understanding which mosquitoes can transmit the virus.
Prof Ball said: "Unfortunately Zika reminds us that there are severe health inequalities around the globe and only when we tackle these will be able to defend ourselves against future viral outbreaks."