U.S. airlines are facing what threatens to be their most serious pilot shortage since the 1960s, with higher experience requirements for new hires about to take hold just as the industry braces for a wave of retirements.

Federal mandates taking effect next summer will require all newly hired pilots to have at least 1,500 hours of prior flight experience—six times the current minimum—raising the cost and time to train new fliers in an era when pay cuts and more-demanding schedules already have made the profession less attractive....