A spokesman for the ministry said the plane was a Trigana Air flight carrying 49 passengers, including two children and three toddlers, and five crew members.
The plane took off from Jayapura at 2:22pm local time (3:22pm AEST) for what should have been about a 40-minute flight to Oskibil.
Air traffic controllers lost contact with the turboprop plane about 30 minutes later at 2:52pm, several minutes before its 3:00pm scheduled time of arrival.
Oksibil is about 40 kilometres from the border with Papua New Guinea and is the capital of the Bintang Mountains Regency.
Bad weather has hampered the search, which has been called off until tomorrow.
“We are not sure what happened to the plane yet and we are coordinating with local authorities,” transport ministry spokesman JA Baratahe said.
“The weather is currently very bad there, it’s very dark and cloudy.
“It’s not conducive for a search. The area is mountainous.”