Common cold accompanied by fever is usually caused by influenza virus. The incubation period of influenza virus depends on the severity of the attack that can be as short as 1 day to a stretched period of 7 days. However, the approximate incubation period is in the range of 1-3 days when caused by influenza virus.uthor Login. The incubation period of a cold ranges between 2-4 days, depending upon the severity of the viral attack. In some cases, it can be as short as 10 hours of infection and as long as 5-7 days. Read the article to know the details.