"Most of the crimes in the city, including targeted killings and other crimes, are carried out using motorbikes," Interior Ministry spokesman Tariq Arian said on April 14.
Motorcycles and scooters are popular in Kabul.
Violators of the ban, which is to take effect immediately, will have their motorcycles seized, the Interior Ministry said.
Delivery riders, who have seen heavy demand since Kabul's coronavirus lockdown, will be exempted.
AFP quoted an unidentified security official as saying that Taliban militants are conducting an increasing number of targeted killings of government officials using motorbikes.
According to the official, street robberies by thieves on motorcycles and scooters are also on the rise.
The decision comes as Kabul, with a population of about 5 million people, is under a three-week lockdown in a bid to contain the spread of the coronavirus in the city.
A total of 714 people in Afghanistan have contracted COVID-19, the disease caused by the virus, according to the Health Ministry. It said the disease had so far killed 23 people in the country.