The Short Version
The claim is directionally supported but misleadingly framed. Most credible sources estimate Alexander's height at roughly 5'3"–5'7" (1.60–1.70 m), while the average Greek male of his era stood approximately 5'6"–5'7" (1.67–1.70 m). The difference — just 2–5 cm in the most careful estimates — falls within the margin of error for ancient textual and skeletal data. Describing Alexander as definitively "shorter than average" overstates what the uncertain evidence actually shows; "at or near average" is more accurate.