Brain dynamics have recently been shown to be modulated by rhythmic changes in female sex hormone concentrations across an entire menstrual cycle. However, many questions remain regarding the specific differences in information processing across spacetime between the two main follicular and luteal phases in the menstrual cycle. Using a novel turbulent dynamic framework, we studied whole-brain information processing across spacetime scales (i.e., across long and short distances in the brain) in two open-source, dense-sampled resting-state datasets. A healthy naturally cycling woman in her early twenties was scanned over 30 consecutive days during a naturally occurring menstrual cycle and under a hormonal contraceptive regime. Our results indicated that the luteal phase is characterized by significantly higher information transmission across spatial scales than the follicular phase. Furthermore, we found significant differences in turbulence levels between the two phases in brain regions belonging to the default mode, salience/ventral attention, somatomotor, control, and dorsal attention networks. Finally, we found that changes in estradiol and progesterone concentrations modulate whole-brain turbulent dynamics in long distances. In contrast, we reported no significant differences in information processing measures between the active and placebo phases in the hormonal contraceptive study. Overall, the results demonstrate that the turbulence framework is able to capture differences in whole-brain turbulent dynamics related to ovarian hormones and menstrual cycle stages.