Introduction Sleep plays an essential role in every individual’s life since it contributes greatly to their well-being and health. Poor sleep quality is one of the most common consequences of hypertension (HTN), which is a leading public health problem. In Ethiopia, it is the main health concern among hypertension patients. Thus, in the study area, there is limited information regarding the investigation of sleep quality among hypertension patients. Therefore, this study aimed to assess sleep quality and associated factors among adult hypertensive patients attending a chronic follow up care clinic in northwest Amhara regional state referral hospitals, Northwest Ethiopia. Methods An institution-based cross-sectional study was conducted among adult HTN patients from March 15/2021 to May 15/2021 in Northwest Amhara Regional State Referral Hospitals. A systematic random sampling method was used to select the study participants. A face-to-face interviewer-administered questionnaire with chart review was used. The Pittsburgh Sleep Quality Index (PSQI) for assessing sleep quality was used in this study. A binary logistic regression was used to see the association between dependent and independent variables. Variables having a p-value < 0.05 with a 95% CI were considered statistically significant in the multivariable logistic regression analysis. Results In this study, 563 hypertensive patients were included, with a response rate of 96.9%. The overall prevalence of poor sleep quality was 37.7% (95% CI: 33.4%–41.6%). Female gender (AOR = 2.55, 95% CI: 1.55–4.18), age ≥ 65 years (AOR = 4.07, 95% CI: 2.07–7.97), overweight (BMI) ≥ 25 kg/m2 (AOR = 1.68, 95% CI: 1.06–2.65), WHO stage II hypertension (AOR = 1.78, 95% CI:1.01–3.12), poor physical activity (AOR = 2.39, 95% CI:1.41–4.05), participants who had depression (AOR = 2.03,95% CI:1.24–3.34) and participants who had anxiety (AOR = 1.89, 95% CI: 1.16–3.03) were factors associated with poor sleep quality. Conclusions In this study, more than one-third of the study participants had poor sleep quality. Female gender, age ≥ 65 years, overweight (BMI) ≥ 25 kg/m2, stage II hypertension, physical inactivity, depression, and anxiety were all associated with poor sleep quality. Managing depression and anxiety disorders, encouraging physical activity, and providing health education about weight loss are all necessary for HTN patients.