The Romanian defence ministry says drone fragments have been found on a farm near the border with Ukraine.
They say the farm is located near the Danube river, which separates Ukraine and Romania at Ukraine's southwestern edge.
Several army search teams were sent to the Great Braila Island to investigate, local media said.
Locals had reportedly heard "strange noises" and shared footage appearing to show the drone falling from the sky.
"On the evening of 28 March, fragments that appear to have come from an aerial device [drone] on a farmland in the Great Braila Island were identified," the defence ministry said.
"The Ministry of National Defence, together with specialised structures within the national defense system, public order and national security, is conducting an investigation of the incident on Friday 29 March according to specific operational procedures."
It comes after authorities in Moldova said three explosions were heard near its border with Ukraine overnight, according to reports in local media.
The explosions appear to have happened in Ukraine's Novodnestrovsk region, just to the north of the Moldovan border, but could be heard from Moldova (see post below).
Ukrainian officials said their forces destroyed 58 Russia-launched attack drones overnight, as well as 26 cruise missiles.