Air India said there were 169 Indian passengers, 53 British, seven Portuguese, and a Canadian.
The plane issued a mayday call and "crashed immediately after takeoff", the Directorate General of Civil Aviation said.
The authority said it crashed outside the airport perimeter.
Ahmedabad, the main city of India's Gujarat state, is home of around eight million people, and the busy airport is surrounded by densely packed residential areas.
Aviation minister Ram Mohan Naidu Kinjarapu directed "all aviation and emergency response agencies to take swift and coordinated action."
"Rescue teams have been mobilised, and all efforts are being made to ensure medical aid and relief support are being rushed to the site. My thoughts and prayers are with all those on board and their families," he added.
"Our thoughts and deepest condolences are with the families and loved ones of all those affected by this devastating event," said the airline chairman.
An emergency centre has been activated and a support team set up for families seeking information, he added.
India has suffered a series of fatal air crashes, including a 1996 disaster when two jets collided mid-air over New Delhi, killing nearly 350 people.
In 2010 an Air India Express jet crashed and burst into flames at Mangalore airport in southwest India, killing 158 of the 166 passengers and crew on board.
Decades earlier, an Air India Boeing 747 flying from Montreal to London in June 1985 crashed into the sea off Ireland with 329 people on board and leaving no survivors.
An Indian commission determined that militant Sikhs had planted a bomb in baggage being carried by the plane.
