The policy is meant to fight environmental pollution and help reduce road accidents, which have been blamed on older cars.
Curbing pollution and improving road safety have become major points of debate in Uganda.
Uganda observed three days of national mourning this week following a bus accident over the weekend, which killed more than 20 people.
Recent surveys have named the capital, Kampala, as one of the most-polluted cities in Africa.
But car importers warn banning old vehicles will lead to job losses and make it harder for poorer Ugandans to afford a car.
A new car, which is often expensive, incurs taxes of more than 50%.
To encourage Ugandans to buy newer cars, lawmakers removed an environmental levy on cars below eight years of age.
Last year, Ugandans imported an average of 2,500 used cars per month.
Neighbouring Kenya stopped the importation of vehicles older than eight years old earlier this year.
Uganda’s parliament has passed legislation banning the import of vehicles older than 15 years.