The final decision on the company's future will be taken next April.
Publishing the preliminary findings of its inquiry into BAA's control of the UK's largest airports, the commission said BAA's current ownership structure was having "adverse consequences" for passengers and airlines.
BAA, owned by Spanish company Ferrovial, has been fiercely criticised for poor customer service and delays at its airports, particularly Heathrow.
The commission said many of the problems of recent years were due to the "common ownership" of Heathrow, Gatwick and Stansted, which account for nearly 90% of departures and arrivals into London.
It will now consult on whether it is appropriate for BAA to have to sell two of its three flagship airports but the disposal of Gatwick and Stansted now looks likely.
BAA chief executive Colin Matthews on the report
Should these two airports be sold, the commission said they should be owned separately in the future to promote competition.
The regulator said BAA had shown a "lack of responsiveness" to the needs of airlines and a "lack of initiative" over expanding capacity.
"This has resulted in investment that is not tailored to the requirements of airport users and lower levels and quality of service for both airlines and passengers," Christopher Clarke, who headed up the inquiry, said.
He added: "BAA has argued that there is no scope for competition to develop so long as there are capacity constraints. We take the opposite view. Unless the market is opened up to competition, there is a serious risk that the current capacity constraints will persist."
The commission said that BAA was likely be allowed to keep control of Southampton and Aberdeen airports as the competition concerns there would be settled by other disposals or were, in Aberdeen's case, caused by particular factors.
BAA's chief executive Colin Matthews said he accepted the report's concerns about "poor service" and "frustration" for passengers.
He declined to comment on the future for individual airports but said BAA had "no intention of selling Heathrow".
He said the break-up of the company could threaten efforts to build new runways at airports in London, seen as vital to boosting passenger capacity and keeping the city competitive as a business location.
"We will continue to point out to the commission the many areas where we believe its analysis is flawed and its remedies would be disproportionate and counter-productive," he said.
The union for aviation specialists challenged the Competition Commission's proposal for BAA to sell off three of its airports.
Garry Graham, aviation secretary for Prospect union, which represents many BAA managerial, technical and support staff, said: "We fear the proposals put forward by the Competition Commission will lead to greater fragmentation and undermine a coherent and strategic approach to service delivery."
He added: "In reality, many of the travelling public have little choice as to the airports they are served by and can use. We question the principle of 'market based solutions' in this context."
And he said there was "clear tension" between the findings of the Competition Commission and government policy as set out in the 2003 Air Transport White Paper.
Airlines applauded the regulator's findings but said the whole regulatory framework of airports needed to be reviewed.
"It is a good start," said Easyjet chief executive Andrew Harrison.
"We are very pleased that the Competition Commission has recognised what is a fundamental problem for UK airports."
Virgin Atlantic said BAA "still acted like a monopoly" and had neglected much-needed improvements at Gatwick, focusing instead on Heathrow.
It called for different companies to be allowed to operate separate terminal buildings at airports such as Heathrow.
"That is the sort of change we need to see," its spokesman said.
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