A police officer told the state news agency that they have been tasked with investigating whether human error was a factor in the crash at Yogyakarta airport on Java island, the country's fourth major plane accident since 2005.
They have not speculated on the cause of the accident, saying they must first interpret data from the jet's flight recorders, or black boxes.
One pilot has reportedly said the plane was hit by a sudden change in wind direction, a phenomenon known as wind shear, as it approached the runway.
Safety low point
One expert said Indonesian air safety has hit a low point after he submitted a report to the president on air travel in the wake of the plane crash.
Oetarjo Diran, a member of a task force appointed by President Susilo Bambang Yudhoyono in January to evaluate transport safety, said they had found weaknesses such as loopholes in regulations and limitations on their enforcement.
"There is still room for improvement," Diran said, less than a week after the Garuda Indonesia jet crash-landed in Yogyakarta.
Last Wednesday's accident was the second fatal airline disaster in Indonesia this year.
An Adam Air plane crashed into the sea on New Year's Day in the earlier tragedy, killing all 102 people on board.
Indonesia has also suffered major ferry disasters in recent months. The total death toll from the worst incidents runs into hundreds and has heaped pressure on politicians to boost safety.
But Diran said that safety was not just a matter of statistics, it was also about the level of risk the public was willing to tolerate.
"Safety is a very abstract concept," he said.
"The acceptable level is actually the level that the general public can bear."