Employers are hiring a record number of seasonal workers for the holidays. Adding a new wrinkle this year, some now will be eligible for paid sick leave benefits—just as flu season arrives.

Holiday workers usually are employed during the fourth quarter of the year—October, November, and December—which is also the height of flu season. While these workers haven’t traditionally qualified for time off for illness, many of the states with new paid sick leave mandates require that seasonal workers be...