Since the government introduced the pass last week, registration to receive the jab has increased fivefold, according to the health minister.
Citizens are now required to present the document for access to all government buildings, as well as spaces such as cafes, restaurants, cinemas, gyms and transportation.
The union of cafe and restaurant owners, the lawyers union, rights organizations and some opposition parties have variously attacked the pass.
It triggered protests on the streets recently, with demonstrators saying that the pass is a violation of the constitution and international laws.
Cafe owner Noreddin said some of his customers left the cafe when he asked for the passes but he did not want to risk having people without documentation in case authorities came to his door.
Morocco has administered doses to 64% of its population using mostly the AstraZeneca, Sinopharm and Pfizer vaccines. It has also started administering booster jabs.