Dry eye disease (DED) is a chronic eye disease and a common complication among the world's population. Evaporation of moisture from tear film or a decrease in tear production leads to an unstable tear film which causes DED. The tear film breakup time (TBUT) test is a common clinical test used to diagnose DED. In this test, DED is diagnosed by measuring the time at which the first breakup pattern appears on the tear film. TBUT test is subjective, labour-intensive and time-consuming. These weaknesses make a computer-aided diagnosis of DED highly desirable. The existing computer-aided DED detection techniques use expensive instruments for image acquisition which may not be available in all eye clinics. Moreover, among these techniques, TBUT-based DED detection techniques are limited to finding only tear film breakup area/time and do not identify the severity of DED, which can essentially be helpful to ophthalmologists in prescribing the right treatment. Additionally, a few challenges in developing a DED detection approach are less illuminated video, constant blinking of eyes in the videos, blurred video, and lack of public datasets. This paper presents a novel TBUT-based DED detection approach that detects the presence/absence of DED from TBUT video. In addition, the proposed approach accurately identifies the severity level of DED and further categorizes it as normal, moderate or severe based on the TBUT. The proposed approach exhibits high performance in classifying TBUT frames, detecting DED, and severity grading of TBUT video with an accuracy of 83%. Also, the correlation computed between the proposed approach and the Ophthalmologist's opinion is 90%, which reflects the noteworthy contribution of our proposed approach.