Background Intestinal parasitosis is a major public health problem that affects the health of primary school children in low- and middle-income countries where water, sanitation, and hygiene (WASH) conditions are deficient. Since there is a paucity of information on the prevalence and associated factors of this problem among primary school children in Dessie City in Ethiopia, this study was designed to address these gaps. Methods A school-based cross-sectional study was conducted among 407 stratified-sampled primary school children in five primary schools at Dessie City from April to June 2018. Data were collected using a pretested structured questionnaire, an observation checklist and laboratory analysis of stool samples. Stool specimen from each study participant was collected using clean, properly labeled and leak-proof stool cup. A portion of stool from each study participant collected sample was processed using saline wet mount technique and examined by microscope. The remaining specimens were preserved with 10% formalin and transported to Dessie Comprehensive Specialized Hospital laboratory to be processed by using formol-ether concentration technique. Then, slide smears were prepared from each processed stool specimen and finally, it was microscopically examined with 10x as well as 40x objectives for the presence or absence of intestinal parasites. Factors significantly associated with intestinal parasitosis were determined using binary logistic regression model at 95% CI (confidence interval). Thus, bivariate (COR [crude odds ratio]) and multivariable (AOR [adjusted odds ratio]) logistic regression analyses were carried out. From the multivariable analysis, variables having a p-value of less than 0.05 were declared as factors significantly associated with intestinal parasitosis among primary school children. Main findings The overall prevalence of intestinal parasitosis was found to be 16.0% (95% CI: 12.5–19.4%), of these, 50.8% were positive for protozoa, 32.2% for helminth infections and 16.9% for double co-infections. Entamoeba histolytica was the most prevalent parasite (29.2%), followed by Giardia lamblia (21.5%), Ascaris lumbricoides (18.5%), Hymenolepis nana (9.2%) and Enterobius vermicularis (4.6%). Prevalence rates were similar among government (16.3%) and private (15.7%) school children. Water consumption was less than 5 liters per capita per day in 4 of the 5 schools. Thirty-eight (9.3%) of primary school students reported that they practiced open defecation. About two-thirds (285, 70.0%) said they always washed their hands after defecation. Mother’s education (illiterate) (AOR = 3.3; 95% CI: 1.20–9.37), father’s education (illiterate) (AOR = 3.9; 95% CI: 1.40–10.82), fathers who could read and write (AOR = 3.3; 95% CI: 1.25–7.86), handwashing before meal (sometimes) (AOR = 2.2; 95% CI: 1.11–4.17) and poor knowledge of WASH (AOR = 9.3; 95% CI: 2.17–16.70) were statistically associated with presence of intestinal parasitic infections. Conclusion We concluded that the prevalence of intestinal parasitosis in the study area among Grades 4–8 primary school children had public health significance. Factors significantly associated with intestinal parasitosis among primary school children’s were illiterate mothers and fathers, irregular handwashing of children before meals, and poor knowledge of WASH. Health education to improve students’ WASH knowledge and mass deworming for parasites are recommended as preventive measures; and improvements to the quality of WASH facilities in primary schools are strongly recommended to support these measures.