Campaigning in Oxford this week, Shapps said: "The benefits of this project were always finely balanced against its costs, both financial and environmental.
"If re-elected we will review as a priority this scheme to ensure that it is still worth going ahead. We will not allow the scheme to proceed if there is not a strong case that it will boost jobs, prosperity and has local support.
"If a majority Conservative government is elected, we will develop this important strategic corridor which will be a driver of future prosperity, investing in the new East-West Rail link, local roads and new cycling schemes."
The Conservatives said the review would focus on the Oxford to Milton Keynes and M1 section of the proposed Oxford-Cambridge Expressway, but an upgrade to the last remaining single-carriageway section, between Caxton Gibbet and the A1 trunk road, would proceed as planned under a Tory government.
The review will be welcomed by environmental campaigners who have been fighting for the project to be scrapped.
In July, the Berks, Bucks and Oxon Wildlife Trust failed to convince a High Court judge that a strategic environmental assessment should have been carried out on the government’s ‘preferred corridor’ for the road.
However, the expressway forms a key element of wider plans for growth in the Oxford to Cambridge corridor, where the National Infrastructure Commission (NIC) has called for one million homes to be developed by 2050.
In March, the NIC warned that key milestones for the growth corridor project were "at risk of being missed", including the development of a spatial vision and the designation of locations for new settlements.
Shapps said: "I am not at all anti-roads and we have got a massive road investment project. I am just not satisfied that this scheme is going to provide the benefits that we first thought.
"Specifically, a lot of it is on flat land which is prone to flooding, so the mitigation measures to protect against that will massively add to the cost of the project.
"I am disappointed with the speed of progress of east-west rail and I think it is by far the better solution to boost the Oxford-Cambridge-Milton Keynes link-up."
In separate news, the regeneration director of one of the councils in the corridor is to leave the authority next year.
Jason Longhurst, director of regeneration and business at Central Bedfordshire Council, made the decision to leave "to pursue his interests in the sustainable growth agenda". He will continue in his position as chairman of the private sector-led UK Business Council for Sustainable Development.