Unite members of the Caterers Offshore Trade Association (COTA) were asked if they would be willing to take action over pay.
The result saw 54.2% of votes back strike action, with 62.7% supporting action short of strike.
Unite urged COTA to return to the negotiating table. Members of the RMT union are also being balloted on the issue.
COTA - which expressed disappointment at the result - indicated earlier this year that it was retracting the second year of a two-year pay deal, worth 1.3%, in an effort to secure jobs.
COTA's chairman, Peter Bruce, said detailed contingency plans had been put in place to deliver at the very least a basic service.
The association urged members of the RMT to reject calls for a strike.
Members of Unite staged protests on Wednesday at several firms connected to offshore catering, ahead of the ballot closing.
A ballot by offshore catering workers has backed strike action.