British Airways said it expected to operate around 85 percent of its scheduled flights at the airport throughout the day.
Restrictions on overnight flights have also been temporarily lifted to help ease congestion, according to the UK's transport department.
Around 230,000 passengers use Heathrow every day -- 83 million a year -- making it one of the world's busiest airports. Planes from Heathrow serve around 80 countries.
The scale of the disruption raised questions about the vulnerability of one of the UK's critical pieces of travel infrastructure.
Fire officials said the fire, which broke out on Thursday night, was "believed to be non-suspicious" and that an investigation would "focus on the electrical distribution equipment".
Earlier, London's Metropolitan Police said the force's Counter Terrorism Command was leading the investigation into the fire given its impact, but that there was "currently no indication of foul play".