John Glen, Conservative MP for Salisbury, said any decision to make the A303 a dual carriageway must include protection for the World Heritage site.
Mr Glen said a tunnel was the only "realistic solution".
A government feasibility study is already under way to consider the various options for the road.
Speaking in a Westminster debate, Mr Glen said the road, which runs from Hampshire to Devon, had become the "devil's highway" and "one of the most notorious traffic blackspots in the country".
He joined other South West MPs calling for the government to consider the wider economic, environmental and safety benefits of improving the road.
However, he cautioned that any plans to turn part, or all, of the 92 mile (148km) road into a dual carriageway must include protection for Stonehenge.
Mr Glen said he had been told by English Heritage, the National Trust and the Council for British Archaeology that Stonehenge would be "formally placed on the at-risk register," if a dual carriageway was constructed close to the historic site without adequate protection.
Plans for a tunnel were initially shelved in 2007 when the government said the estimated cost of Â£510m was too expensive.
"A poorly designed and badly executed" dual carriageway which could "undermine a 5,000 year old world heritage site is not an improvement worth fighting for," Mr Glen said.
Transport Minister Robert Goodwill said the government hoped an announcement on the future of the A303 would be made in the autumn.
A Wiltshire MP has reignited calls for a tunnel to be constructed alongside the Stonehenge monument.