The episode on Tuesday saw two vehicles from the Special Monitoring Mission (SMM) stopped by an armed man in "military-style clothing with no markings" at a known Ukrainian army position, the OSCE said.
"When one of the SMM monitors stepped out of the vehicle to speak with the man, the latter chambered a round into his submachine gun... and after removing the weapon's safety, pointed it at the SMM monitor and put his finger on the trigger," a statement said.
The monitor requested that the man call his commander, which he did, speaking on his radio while continuing to point his gun at the monitor. Another man then arrived carrying an AK-47 assault rifle.
"He was accompanied by three other armed men carrying assault rifles, some of whom appeared to be intoxicated, and appeared to be in a position of authority," the OSCE said.
"Using Russian and speaking in an aggressive manner, the man said that he and the other armed men present were members of the Ukrainian Armed Forces," it said.
Some of the men were dressed in military-style clothing.
The monitor asked the man who appeared to be in charge to order the gunman to lower his weapon. The armed man obeyed but without making his gun safe. After around 15 minutes the monitors were allowed to leave.
The OSCE, which has around 590 staff in eastern Ukraine monitoring a conflict that has killed nearly 9,500 people since April 2014, has regularly complained about interference, intimidation and threats to monitors' safety.
Ukraine and the rebels -- who the West accuses Russia of directing -- have agreed a series of ceasefires but they have failed to halt the violence. A peace deal has floundered and the OSCE says both sides seem to be bringing up more hardware.