The DH8 was 150m (500ft) over the school near Birmingham Airport last September when the pilot saw the drone about 500m (1,640ft) away.
Despite the near miss, the flight was able to go on to land, the UK Airprox Board (UKAB) said.
West Midlands Police were unable to locate the drone or its operator.
More updates on this and other stories in Birmingham and the Black Country
The UKAB report into the incident on at 0904 BST on 7 September concluded: "Members agreed that the drone operator, by operating at that position and altitude on the approach path to Birmingham airport, had flown the drone into conflict and had endangered the DH8 and its passengers."
But it added that "on this occasion the drone had passed sufficiently clear such that there was no risk of collision".
The school was contacted as officials said they had not been advised of the drone operation in advance.
There have been 60 "near misses" between aircraft and drones in past 12 months, UKAB figures show.
Civil Aviation Authority (CAA) rules state drones must not be flown above 400ft or near airports or airfields.
It launched a new website to publish its revised code of conduct for drones, labelled the dronecode, in November.
A drone "endangered" an aircraft and its passengers when it was flown near the plane a few hundred feet above a primary school, a report has said.