Alinda Capital Partners - a US firm that specialises in infrastructure - will pay 325m euros ($441m, Â£282m).
The deal will boost Ferrovial's accounts. It cuts the Spanish owner's stake in BAA to 49.99%, meaning it no longer has to include the UK firm's debts on its balance sheet.
The deal puts a much higher value on BAA than analysts had expected.
"This sale is in line with our strategy to establish a market valuation of our assets," said Ferrovial chief executive Inigo Meiras.
The transaction values BAA - which operates Heathrow, Stansted, Glasgow, Edinburgh, Aberdeen and Southampton airports - at Â£4.8bn.
That was more than double consensus, according to news agency Reuters, and news of the sale sent Ferrovial's share price more than 5% higher in morning trading.
However, it is still considerably lower than the Â£10.3bn valuation at which Ferrovial originally bought BAA in 2006.
BAA's value had been damaged by a decision by the UK's Competition Commission that BAA's dominance of air traffic into and out of Scotland and London was unacceptable.
This had already forced BAA's sale of Gatwick Airport, with Stansted and one of Edinburgh and Glasgow set to follow.
By reducing its ownership of BAA to a fraction below 50%, Ferrovial also no longer needs to consolidate its UK subsidiary into its accounts - meaning that it no longer has to include BAA's debts as part of its own.
The accounting rule means that Ferrovial's reported debts will fall by almost three-quarters, from 19.75bn to 5.2bn euros.
However, Ferrovial's remaining stake still leaves it as by far the biggest single investor in BAA, with effective control over the firm.
The Spaniards had been openly seeking a buyer for up to 10% of BAA for a year.
The infrastructure company said the sale proceeds would be used to fund other investments.
Spanish infrastructure firm Ferrovial has sold 5.9% of Heathrow Airport-operator BAA to an investment fund.