The OU wants to close seven regional centres, in Bristol, Birmingham, Cambridge, Gateshead, Leeds, London and Oxford, to streamline student support.
The university's senate, which met on Wednesday, voted to reject the plan.
The University and College Union (UCU) says more than 500 jobs are at risk. The ballot closes on 5 November.
UCU Open University branch president Pauline Collins said: "Axing over 500 staff across seven centres would be catastrophic to the Open University's ability to provide the kind of support that students need.
"We hope the university will now see sense and work with us to find a better solution for staff, students and the future of the Open University."
The OU said the offices earmarked for closure were not predominantly used as teaching centres and services to students would not be reduced or withdrawn.
The new structure, due to be in place by February 2017, would retain offices in Belfast, Cardiff, Edinburgh, Milton Keynes, Manchester and Nottingham, as well as a small sub-office in Dublin.
The university said its centres in Milton Keynes, Manchester and Nottingham would expand under the plan.
Peter Horrocks, Vice-Chancellor, said: "The OU's mission has always been about embracing innovation and providing our students with the best possible experience.
"This is a difficult decision and I fully recognise the impact it will have on many of our staff, but we cannot afford to stay still.
"This recommendation, if approved, would allow us to enhance student support in a way that's simply not possible in our current office network, and offer our students the sort of support they expect and deserve."
A final decision will be made by the university's council in late November. If approved, a period of consultation with unions would follow.
The OU has almost 200,000 students, with many combining their study with employment and other commitments.
The Open University (OU) staff are being balloted for strike action in a row over job losses and the closure of regional offices.