A fire at the North Hyde electrical substation in Hayes, west London, knocked out the power supply to Heathrow and other businesses and homes in the surrounding area.
The cause of the fire is not yet known, but emergency services were first called to the scene at 23:23 GMT on Thursday.
Energy Secretary Ed Miliband told the BBC the fire appeared to have knocked out a backup generator as well.
Heathrow has said it doesn't "have clarity on when power may be reliably restored", and that it will be closed until 23:59 tonight.