Releasing details of the ballot on Thursday, the Unite union said that it will decide on Monday what action it will take to allow time for last-minute negotiations with BAA - leaving thousands of people with summer vacation bookings to sweat over the weekend.
BAA has warned that any walkouts will force it to close its airports, which include Heathrow, Stansted, Glasgow and Edinburgh, because the potential strikers include essential workers like firefighters, security guards and engineers.
Analysts have speculated that Unite will select the August bank holiday weekend - the last weekend of the month - to maximise disruption.
The move is unlikely to endear BAA's staff to the public in a year that's already seen significant travel chaos thanks to the Icelandic volcanic ash cloud and a series of rolling British Airways strikes.
Prime Minister David Cameron has warned that a walkout would achieve nothing "apart from damage to business, damage to jobs, damage to the interests of tourists who want to come to visit Britain, or people who want to leave Britain and have a holiday overseas."
"We want to demonstrate that Britain is open for business," Cameron said ahead of the results of the ballot.
Heathrow is the world's busiest international airport, while Stansted is the country's busiest low-cost hub.
"The travel industry is already experiencing a marked decline in bookings this year, so strike action like this will do nothing to appease that," said Bob Atkinson, a travel analyst at travelsupermarket.com.
Workers are unhappy with BAA's offer of a 1 percent pay raise this year after accepting a pay freeze last year.
BAA said it made a reasonable offer given a decline in passengers because of the recession and the volcanic ash cloud disruption.
The company added it believed the ballot did not provide a clear mandate for strike action because only around half the eligible workers voted - 74.1 percent of the 3,054 staff who voted said yes to strike action, but a total of 6,185 workers were balloted.
"We regret the uncertainty this vote has already caused our passengers and airline customers," BAA said in a statement. "We hope that the union will engage with us quickly to conclude an agreement."
Unite national officer Brendan Gold said it was not the "intention" of the union to ruin people's vacations and said the public should question "why BAA has let this run on for four months."