Until recently, preclinical and clinical work on diabetes has focused on the understanding of blood glucose elevation and its detrimental metabolic sequelae. The advent of continuous glucose monitoring (CGM) technology now allows real time monitoring of blood glucose levels as a time series, and thus the exploration of glucose dynamics at short time scales. Previous work has shown decreases in the complexity of glucose dynamics, as measured by multiscale entropy (MSE) analysis, in diabetes in humans, mice, and rats. Analyses for non-human primates (NHP) have not been reported, nor is it known if anti-diabetes compounds affect complexity of glucose dynamics. We instrumented four healthy and six diabetic rhesus monkeys with CGM probes in the carotid artery and collected glucose values at a frequency of one data point per second for the duration of the sensors' life span. Sensors lasted between 45 and 78 days. Five of the diabetic rhesus monkeys were also administered the anti-diabetic drug liraglutide daily beginning at day 39 of the CGM monitoring period. Glucose levels fluctuated during the day in both healthy and diabetic rhesus monkeys, peaking between 12 noon - 6 pm. MSE analysis showed reduced complexity of glucose dynamics in diabetic monkeys compared to healthy animals. Although liraglutide decreased glucose levels, it did not restore complexity in diabetic monkeys consistently. Complexity varied by time of day, more strongly for healthy animals than for diabetic animals. And by dividing the monitoring period into 3-day or 1-week subperiods, we were able to estimate within-animal variability of MSE curves. Our data reveal that decreased complexity of glucose dynamics is a conserved feature of diabetes from rodents to NHPs to man.