The Auckland Council-controlled agency plans to remove a tall manuka tree shielding the graves from traffic noise and erect a retaining wall against the 3.5m-high cut it has made.
Plans show a "worst-case scenario" in which excavation will go as close as 915mm to Fairburn's grave.
Mrs Holman said that after an on-site meeting with the agency's project manager, she and her sister remained appalled at such an insensitive proposal
"The face of the retaining wall will be about two metres from the grave.
"The headstone faces the road to reflect the fact that Rex often challenged conventions.
"But when we buried him we did not think it would be right on a motorway.
"Students come here to see his grave, too, and we would not be able to stand where we do when the wider road goes through.
"Our grandmother was buried in the same grave in 1959."
Fairburn, whose first poem was published in 1927, died in 1957.
The sisters did some research on their forbears' rights to be left in peace in what is now a closed cemetery and a place of historic interest.
In the Burial and Cremation Act they found the line: "A closed cemetery shall not be sold or leased or otherwise disposed of, or diverted to any other purpose."
They said several other graves near the roadside were also affected.
Auckland Transport said the land for the road widening was bought some years ago from the North Shore City Council, and all work would be in the reserve outside the cemetery boundary.