Approaches to foster motor creativity differ according to whether creative movements are assumed to be enacted creative ideas, or solutions to emerging motor problems that arise from task and environmental constraints. The twofold aim of the current study was to investigate whether (1) an enriched physical education (PE) intervention delivered with a joint constraints-led and cognitive stimulation approach fosters motor creativity, and the responsiveness to the intervention is moderated by baseline motor and cognitive skills and sex; (2) the intervention may benefit motor creativity through gains in motor coordination, executive function, and creative thinking. Ninety-five children, aged 6–9 years, participated in a 6-month group randomized trial with specialist-led enriched PE vs. generalist-led conventional PE. Before and after the intervention, Bertsch’s Test of Motor Creativity, Movement Assessment Battery for Children, Random Number Generation task and Torrance Test of Creative Thinking were administered. Linear mixed models were run accounting for the random effects of data clusters. Multiple mediation analysis was performed to assess whether motor coordination, executive function and creative thinking mediated any improvement of motor creativity. Results showed that (1) specialist-led enriched PE, compared to generalist-led conventional practice, elicited a more pronounced improvement in all motor creativity dimensions (fluency, flexibility, and originality) independently of baseline levels of motor and cognitive skills and sex; and (2) improved motor creativity was partially mediated by improved motor coordination and, as regards motor flexibility, also by improved inhibitory ability. In conclusion, enriching PE with tailored manipulations of constraints and variability may enhance the ability to create multiple and original task-pertinent movements both directly and through indirect paths. The results are discussed extending to motor creativity a theoretical framework that distinguishes different creativity modes. The intervention may have fostered the generation of creative movements directly through the exposure to variation in constraints, activating the sensorimotor ‘flow’ mode of creativity that bypasses higher-order cognition, but also indirectly through a systematic and conscious convergence on solutions, activating the ‘deliberate’ mode of creativity that relies on inhibition to reject common or task-inappropriate movement categories.