Child care providers statewide are cautiously bracing to support the children of essential workers including hospital staff and grocery workers as Gov. Charlie Baker orders most child-care centers closed beginning Monday.

At least a dozen Boston-area center and home-based child-care programs will remain open as exempt emergency programs.

“We have to prioritize,” Alex Chibasky, manager of School is Cool centers across Massachusetts, said Sunday. “It depends on demand and we do have quite a few calls and emails. We plan to staff our rooms appropriately.”

The state order gives child care service priority to workers including emergency responders, law enforcement, transportation and infrastructure workers, sanitation workers and families living in shelters and others for whom no other options exist.

Some local home-based centers won’t feel much of a disruption, as laws still limit the number of children any center can care for.

“My space will not be overwhelmed. I think I will be OK,” Joycelyn Browne, who runs a home-based center in Dorchester, said. Browne’s center was among four listed as emergency exempt in Dorchester.

Baker’s office released a 10-page web listing of all child-care centers on the mass.gov website that are exempt from the closure order, with some communities only listed as having one center open for the town. The Department of Early Education and Care will implement procedures to quickly review child care applications and background checks for staff.

Chibasky said the aid for parents in essential workforce positions won’t do much to quell their anxieties.

“It’s not about the parents working from home, it’s more the anxiety,” Chibasky said. “they’re just scared to go outside and get exposed.”