Members of the University and College Union are staging a one-day strike with a further walk-out planned at the Oxford regional centre on 2 December.
The university council met on Tuesday to agree the restructuring plans.
The centres set to shut are in Birmingham, Bristol, Cambridge, Gateshead, Leeds, London and Oxford.
Staff in Belfast, Cardiff, Edinburgh, Milton Keynes, Manchester and Nottingham are also joining the strike.
The union said the student support centre closures would put 502 jobs at risk.
The OU wants to centralise its support centres in three locations: Manchester, Nottingham and Milton Keynes.
Union branch president for the university, Pauline Collins, said: "Nobody wants to take strike action, but we have now been left with no alternative. The university needs to listen to our concerns and abandon these damaging proposals."
Peter Horrocks, vice-chancellor of The Open University, said the decision meant "much-needed improvements" could be made to student support services, which had not been possible across smaller, dispersed offices.
"Our priority now is to maintain and improve services for our hard-working students while supporting our staff as we start to implement these changes," he said.
Open University (OU) staff have gone on strike after the institution said it would press ahead with plans to close seven regional centres.