The Airbus A320 – flight 4U 9525 – went down between Digne and Barcelonnette. There are no survivors, officials say.
The “black box” flight recorder has been found, the French interior minister says. The cause of the crash is not known and the plane did not send a distress signal.
The dead are believed to include 16 German schoolchildren and two babies.
French and German leaders have expressed shock.
“This is the hour in which we all feel deep sorrow,” German Chancellor Angela Merkel told reporters, adding that she was planning to travel to the crash site.
Gilbert Sauvan, a local council official, told Les Echos newspaper that the plane had “disintegrated”.
“The largest debris is the size of a car,” he said.
The passengers included a German school class on its way back from an exchange trip.
Sandrine Boisse, a tourism official from the ski resort of Pra Loup, told the BBC that she had heard a strange noise in the mountains at around 11:00 (10:00 GMT).
“At first we thought it was on the ski slopes, an avalanche, but it wasn’t the same noise,” she said. “I think it was the noise of when a plane goes very quickly down.”
The plane began descending one minute after it reached its cruising height and continued to lose altitude for eight minutes, Germanwings managing director Thomas Winkelmann told reporters.
He said the aircraft lost contact with French air traffic controllers at 10:53 at an altitude of about 6,000 feet.
The plane did not send out a distress signal, officials said. Earlier reports of a distress call, quoting the French interior ministry, referred to a message from controllers on the ground.
The White House has said there is no evidence so far of a terror attack.
French Prime Minister Manuel Valls said he had sent Interior Minister Bernard Cazeneuve to the scene, and a ministerial crisis cell had been set up to co-ordinate the incident.
The interior ministry said debris had been located at an altitude of 2,000m (6,500ft).
Spokesman Pierre-Henry Brandet told BFM TV that it would be “an extremely long and extremely difficult” search-and-rescue operation because of the remote location.
Spain’s King Felipe, on a state visit to France, thanked the French government for its help and said he was cancelling the rest of his visit.
The Airbus A320 is a single-aisle passenger jet popular for short- and medium-haul flights.
Although it began its life as an independent low-cost carrier, Germanwings is wholly owned by its parent Lufthansa.
It operates increasing numbers of the group’s point-to-point short-haul routes and takes many passengers from German cities to Mediterranean sunspots.
A statement posted on the airline’s website reads “We must confirm to our deepest regret that Germanwings Flight 4U 9525 from Barcelona to Düsseldorf has suffered an accident over the French Alps. The flight was being operated with an Airbus A320 aircraft, and was carrying 144 passengers and six crew members.
“Lufthansa and Germanwings have established a telephone hotline. The numbers 0800 014 8904 (UK) and +1 407 362 0632 (worldwide) are available to all the families of the passengers involved for care and assistance.
“Everyone at Germanwings and Lufthansa is deeply shocked and saddened by these events. Our thoughts and prayers are with the families and friends of the passengers and crew members.
“Germanwings is conducting a full investigation.”