This study aimed to evaluate the frequency of sleep and eating problems in children with autism spectrum disorder (ASD), the factors associated with these problems, and the relationship with the risk of developing depression and anxiety in their parents. In the study, 156 children with ASD and their parents were included. The Brief Autism Mealtime Behavior Inventory (BAMBI), the Children's Sleep Habits Questionnaire (CSHQ), the Hospital Anxiety Depression Scale (HADS) were completed by the parents. The Childhood Autism Rating Scale (CARS) was administered by the researchers to evaluate the severity of ASD in children. The mean age of children was 8.08 ± 2.84, and 87.2% of the children were male. The mean score of CARS was 41.25 ± 6.16, the mean score of BAMBI was 45.67 ± 11.87, and the mean score of CSHQ was 51.67 ± 10.17. According to the CSHQ, 83.3% of the children had sleep problems. The response rate above the cut-off point in the HAD-A subscale was 59.6%, whereas it was 67.3% in the HAD-D subscale. There was a positive correlation between CARS and BAMBI, CSHQ, HAD-A, and HAD-D subscales. There was a positive correlation between BAMBI and CHSQ, HAD-A, and HAD-D subscales. There was a positive correlation between the CSHQ, HAD-A, and HAD-D subscales. There was a negative correlation between the age of the child with ASD, food refusal, and resistance to bedtime. As sleeping and eating problems affect a large portion of children diagnosed with ASD and their caregivers, large population-based studies evaluating both these problems must be designed and carried out to understand factors affecting the prevalence, development, and persistence of sleeping and eating problems and to determine interventions to reduce these issues.