Visitors to the county council’s buildings will be required to continue wearing a mask or other face-covering from Monday (July 19).
The local authority said the precaution should help protect customers and staff from Covid-19 while in enclosed public spaces at council sites, including libraries.
Officials added that they considered public safety to be the council’s priority, especially for the most vulnerable.
Lower infection rates, they believe, will also help the council maintain its services to the public by keeping staff levels high.
The called the requirement (unless exempt) part of a "responsibly cautious approach" outlined by the Prime Minister in announcing the end of legal restrictions from Monday.
It will also apply to people joining ceremonies led by a registrar from the county council.
Darrell Gale, Director of Public Health for East Sussex, said:
“Wearing face-coverings offers some additional protection from catching and passing on the virus.
"That’s why visitors to the county council’s buildings and people taking part in wedding ceremonies where we officiate are urged to continue to wear a face-covering.
“We want to keep everyone in our communities as safe as possible and we want to ensure that public services aren’t weakened by high levels of infection and illness.
"Our thanks to everyone in our communities who continues to play their part in protecting each other.”