WASHINGTON—Many American households remain financially fragile and uncertain about their retirement prospects despite a booming job market that is lifting wages, according to a Federal Reserve survey released Thursday.

One-quarter of working individuals say they have no retirement savings at all, the survey said, and 44% worry that their saving isn’t on track. Among younger workers, aged 18 to 29, 42% have nothing set aside, and only 26% believe they are adequately prepared for retirement.

Households...