The Civil Aviation Authority of Vietnam said in a statement on its website late Tuesday that it had recommended that the sleeping controller and one other controller also be fined.
The statement said the incident was a threat to safety, adding that the head of the air traffic control was also suspended.
The online Dan Tri newspaper reported that the crews on two flights of budget airline Vietjet Air- one departing for South Korea and one arriving from Ho Chi Minh City - could not contact the air traffic control at Cat Bi international airport in northern city of Hai Phong for 33 minutes on March 9.
The newspaper said one controller was absent while the main air traffic controller was sleeping. A technician was also suspended.
The flights were eventually able to depart and land successfully.