Youngsters close to the age of three who develop wheezing with the virus have a 30-fold risk of becoming asthmatic by the time they turn six.
The older the toddlers are when they catch the virus, the greater their chance of developing the condition, which is called Rhinovirus, according to the research.
Around 5 million people in Britain, including more than 1m children, suffer from asthma.
Daniel Jackson, from the University of Wisconsin, who led the team which carried out the study, said that the Rhinovirus was a “significant predictor” that children would go on to become asthmatic.