A booming tech industry and strong job market have fueled an apartment-building frenzy in the midsize, mile-high city of Denver. Neighborhoods once filled with rundown 19th-century warehouses, modest apartment complexes and vacant lots have transformed into landscapes of glass, brick and steel, as new structures continue to climb.

Standing on the 12th-floor roof deck of the Alexan Uptown, a new 372-unit luxury apartment building, real-state agent Justin De La O counts about half a dozen cranes within a few blocks’ radius...