The German carmaker wants to close two final salary schemes and consolidate all staff to a less generous provision that new starters have been on since 2014.
BMW creates more than 200,000 Minis a year at its Oxford plant, and walkouts would be another headache for the embattled UK car industry.
Unite has described the closure of the final salary pension scheme as "pensions robbery".
"BMW bosses would do well to heed the growing sense of betrayal over their broken pension promises, which have already seen 96 per cent of workers saying they would take industrial action in a consultative ballot," Unite general secretary Len McCluskey said in a statement.
Taking part in the ballot are around 4,500 Unite members workers who are part of the BMW occupational pension scheme at five British sites. The vote due to close 31 March.