Residents of The Villages, a sprawling retirement community in central Florida, were still gathering in town squares, visiting nail salons and browsing an estate sale in late March. Only after Gov. Ron DeSantis issued a statewide stay-at-home order April 1 did many of the holdouts hunker down, residents and officials say.

The delay in adopting social-distancing measures could haunt The Villages, a fast-growing metro area of more than 128,000 people whose older age makes them especially vulnerable to Covid-19, the disease caused...