The Food and Drug Administration says the illnesses are linked to salmonella-tainted eggs from Gravel Ridge Farms, which is north of Birmingham in Cullman.
The agency issued a recall notice last month, and it provided an update Tuesday.
The FDA says 10 people were hospitalized after coming in contact with cage-free eggs from the farm, but no one has died.
The government says recalled eggs were sold to several grocery stores in Georgia, Tennessee, and Alabama.
Most of the illnesses are in Tennessee, where 23 people have been affected. Alabama has had seven cases and Ohio has four. Single cases have occurred in Colorado, Iowa, Kentucky and Montana.