Contact was lost with the Trigana Air ATR 42 turboprop just before 15:00 local time (06:00 GMT) after take-off from Sentani airport in the regional capital Jayapura.
The plane was en route to the town of Oksibil in the south of the region.
It is carrying 44 adult passengers, five children and infants, and five crew.
The plane took off from Sentani at 14:21 and contact was lost at 14:55.
Transport ministry spokesman Julius Barata confirmed the disappearance.
"We are not sure what happened to the plane yet and we are co-ordinating with local authorities," he told AFP news agency.
"The weather is currently very bad there, it's very dark and cloudy. It's not conducive for a search. The area is mountainous."
Correspondents say Indonesia has a patchy aviation record, with two major crashes in the last year.
Indonesian plane missing over Papua region - BBC News