The relationship between sleep (caregiver-reported and actigraphy-measured) and other caregiver-reported behaviors in children and adults with autism spectrum disorder (ASD) was examined, including the use of machine learning to identify sleep variables important in predicting anxiety in ASD. Caregivers of ASD (n = 144) and typically developing (TD) (n = 41) participants reported on sleep and other behaviors. ASD participants wore an actigraphy device at nighttime during an 8 or 10-week non-interventional study. Mean and variability of actigraphy measures for ASD participants in the week preceding midpoint and endpoint were calculated and compared with caregiver-reported and clinician-reported symptoms using a mixed effects model. An elastic-net model was developed to examine which sleep measures may drive prediction of anxiety. Prevalence of caregiver-reported sleep difficulties in ASD was approximately 70% and correlated significantly (p < 0.05) with sleep efficiency measured by actigraphy. Mean and variability of actigraphy measures like sleep efficiency and number of awakenings were related significantly (p < 0.05) to ASD symptom severity, hyperactivity and anxiety. In the elastic net model, caregiver-reported sleep, and variability of sleep efficiency and awakenings were amongst the important predictors of anxiety. Caregivers report problems with sleep in the majority of children and adults with ASD. Reported problems and actigraphy measures of sleep, particularly variability, are related to parent reported behaviors. Measuring variability in sleep may prove useful in understanding the relationship between sleep problems and behavior in individuals with ASD. These findings may have implications for both intervention and monitoring outcomes in ASD.