An American man was killed and a German woman was injured on Sunday morning, a spokesman for Austria's foreign ministry said, Reuters reported.
Austria holds the rotating presidency of the Organization for Security and Cooperation in Europe (OSCE).
Read alsoOSCE SMM car damaged in anti-tank mine blast in Donbas, casualties reportedThe Ukrainian military said the incident took place at 10:17 local time (0717 GMT) near the small village of Pryshyb, which is controlled by pro-Russian separatists.
The unarmed, civilian OSCE mission with more than 700 international observers was deployed in 2014. The role of the monitors includes verifying the withdrawal of heavy weapons as agreed under the 2015 ceasefire agreement.
Austrian Foreign Minister Sebastian Kurz called for an investigation of the incident and, in a tweet, said he had spoken to the mission's ambassador, Ertugrul Apakan.
"Need thorough investigation; those responsible will be held accountable," he said on Twitter.
A spokesman for the OSCE said further information would be released as it became available.
The 57 member states of the OSCE, which include Ukraine, Russia and the United States, in March extended its monitoring in Ukraine by a year.