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.

Ms Hyslop is to undertake "an intensive week of activity" focusing on business, trade, tourism, education and culture.
She will meet business leaders in Tokyo and Nagasaki to promote Scotland as a place to invest and do business.
The cabinet secretary said Japan was "a very important international partner for Scotland".
The Scottish government said Japan was one of the top 20 destinations for Scottish exports, and was the seventh largest source of foreign direct investment with Japanese firms employing 6,250 people in Scotland.
Ms Hyslop, who previously visited Japan in 2015, will meet senior figures from companies which are already investing in Scotland, such as Mitsubishi, life sciences firm Kyowa Hakko Kirin and medical firm Reprocell.
She said: "Scotland and Japan have much in common - a wealth of expertise, a passion for innovation, a highly educated and skilled workforce, and a desire for increased international collaboration across all sectors.
"There will be much to share and much to discuss during my time there, including providing reassurance that, despite the UK's vote to leave the EU, Scotland remains a progressive, outward-looking internationalist country that is open for business and ripe for investment.
"I'm confident our dialogue will deliver mutual benefits."

Striker Emmanuel, 27, scored 19 goals in the National League for Bromley last season and played for the Whites between 2012 and 2014.
Centre-back Howlett-Mundle, 19, has previously had spells at Crystal Palace and Scottish sides Hearts and Montrose.
Forward Jackson Jr, 19, had stints at Whitstable Town and Worthing last season and has agreed a two-year deal.
Meanwhile, 32-year-old former Welling player-manager Loui Fazakerley, who is a fitness coach at Crabble, has been registered as a player for the coming campaign.
Find all the latest football transfers on our dedicated page.

A selection of photos from Africa and of Africans elsewhere in the world this week:
Open University (OU) staff have gone on strike after the institution said it would press ahead with plans to close seven regional centres.
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Scottish External Affairs Secretary Fiona Hyslop is to travel to Japan to promote the message that Scotland is "open for business".
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Dover Athletic have re-signed Moses Emmanuel and brought in Jahmal Howlett-Mundle and Ira Jackson Jr.
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Images courtesy of AFP, AP, EPA, Getty Images and Reuters