It aims to alleviate pressure through the pandemic and future seasonal demand.
The facility, at the John Radcliffe Hospital, will have 48-beds for specialist and critical care.
The five-storey building will also have improved storage facilities, a seminar room, a staff room, and additional office space.
It is part of a longer-term plan to expand and improve facilities at the John Radcliffe.
The building will be adjacent to the Trauma Building and the OxSTaR Centre.
Dr Bruno Holthof, Chief Executive Officer at OUH said "We are incredibly pleased about this new building. Not only will it improve our critical care environment, but it will help us in planning for future demands on our services."
Sam Foster, Chief Nursing Officer at OUH, said: "We pride ourselves on the outstanding critical care we give to our most sick patients - and this brand new facility will enable us to improve this even further and provide the best quality of compassionate and excellent care - both now and importantly in the future."
The facility should be finished later this year.
It is supported by Department of Health and Social Care financing.
Minister for Health Edward Argar said: "We're helping the NHS build back better by investing in the future of our hospitals.
"This new critical care building will help John Radcliffe Hospital to continue to deliver world-class care to its patients. The additional surge capacity will enhance their ability to respond to seasonal pressures - something that has proved crucial during this pandemic.
"It's great news for Oxford and all those served by John Radcliffe Hospital that we're backing the £29 million new facility as part of our record investment in our NHS buildings, alongside work to deliver 40 new hospitals across the country by 2030, and another example of this Government backing our public services."