Researchers say the rhinovirus could jump-start the body's antiviral defences, providing protection against the flu.
The findings help answer a mystery surrounding the 2009 H1N1 swine flu pandemic, when an expected surge in swine flu cases never materialised in Europe during autumn.
A Yale University team led by Dr Ellen Foxman studied three years of clinical data from more than 13,000 patients seen at Yale New Haven Hospital with symptoms of respiratory infection.
They found that even during months when both viruses were active, if the common cold virus was present, the flu virus was not.
Dr Foxman, assistant professor of laboratory medicine and immunobiology and senior author of the study, said: "When we looked at the data, it became clear that very few people had both viruses at the same time."
But she added that it is not known whether the annual seasonal spread of the common cold virus will have a similar impact on infection rates of those exposed to the coronavirus that causes Covid-19.
Dr Foxman said: "It is impossible to predict how two viruses will interact without doing the research."
In order to test how the rhinovirus and influenza virus interact, the researchers created human airway tissue from stem cells that give rise to epithelial cells, which line the airways of the lung and are a chief target of respiratory viruses.
They found that after the tissue had been exposed to rhinovirus, the influenza virus was unable to infect the tissue.
"The antiviral defences were already turned on before the flu virus arrived," Dr Foxman said.
According to the study, published in The Lancet Microbe, the presence of rhinovirus triggered production of the antiviral agent interferon, which is part of the early immune system response to invasion of pathogens.
The researchers are now looking at whether introduction of the cold virus before infection by the Covid-19 virus offers a similar type of protection.
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