Background Poor menstrual hygiene practices influence school girls’ dignity, well-being and health, school-absenteeism, academic performance, and school dropout in developing countries. Despite this, menstrual hygienic practices are not well understood and have not received proper attention by school WASH programs. Therefore, this study examined the extent of good menstrual hygiene practices and associated factors among high school girls in Dessie City, Amhara Region, northeastern Ethiopia. Methods A school-based cross-sectional study was employed to examine 546 randomly selected high school students in Dessie City, northeastern Ethiopia. Pretested interviewer-administered questionnaires and a school observational checklist were used for data collection. EpiData Version 4.6 and the Statistical Package for the Social Sciences Version 25.0 were used for data entry and analysis, respectively. Bivariate and multivariable logistics regression analyses were employed to identify factors associated with good menstrual hygiene practices. During bivariable analysis, variables with P-values less than 0.25 were retained for multivariable analysis. In the multivariable analysis, variables with a P-value less than 0.05 were declared to be significantly associated with good menstrual hygiene practices. Results Of the respondents, 53.9% (95% CI [49.6, 58.2]) reported good menstrual hygiene practices. The following factors were found to be significantly associated with good menstrual hygiene practices: age range 16–19 years (AOR = 1.93, 95% CI: [1.22–3.06]); school grade level 10 (AOR = 1.90, 95% CI: [1.18–3.07]); maternal education (primary) (AOR = 3.72, 95% CI: [1.81–7.63]), maternal education (secondary) (AOR = 8.54, 95% CI: [4.18–17.44]), maternal education (college) (AOR = 6.78, 95% CI: [3.28–14.02]) respectively]; having regular menses [AOR = 1.85, 95% CI: (1.03–3.32); good knowledge regarding menstruation (AOR = 2.02, 95% CI: [1.32–3.09]); discussing menstrual hygiene with friends (AOR = 1.79, 95% CI: [1.12–2.86]), and obtaining money for pads from the family (AOR = 2.08, 95% CI: [1.15–3.78]). Conclusion We found that more than half of high school girls had good menstrual hygiene practices. Factors significantly associated with good menstrual hygiene practices include high school girls age 16–18 years, girls grade level 10, maternal education being completed primary, secondary and college level, having regular menses, good knowledge regarding menstruation, discussing menstrual hygiene with friends and obtaining money for pads from the family. Therefore, educating of high school student mothers about MHP should be a priority intervention area to eliminate the problem of menstrual hygiene among daughters. Furthermore, in order to improve the MHP among high school girls, further attention is needed to improving knowledge regarding menstruation among high school girls, encouraging high school girls’ families to support their daughters by buying sanitary pads and promoting discussions among friends about menstrual hygiene. Schools need to focus on making the school environment conducive to managing menstrual hygiene by increasing awareness of safe MHP and providing adequate water/sanitation facilities.