The BBC said the stone marking the author's grave is etched with the warning:
"Blessed be the man that spares these stones/ And cursed be he who moves my bones"Neither the stones nor the bones will be moved during the restoration, the report said.
"We're avoiding the curse," Ian Stainburn, of Stainburn Taylor architects and historic buildings consultants, told the BBC.
"Over the years, the 400 years, (the stones have) started to laminate, the surfaces are coming off, and with people walking over them, clergy during the communion services and so on, the surfaces are getting eroded."
Shakespeare was baptized at Holy Trinity in April 1564 and buried there 52 years later.
His grave slab in the chancel and a memorial to him are popular tourist attractions, the BBC said.