The video, in which militants call Christians "crusaders" who are out to kill Muslims, showed about 15 men being beheaded on a beach and another group of the same size being shot in the head in a patch of scrubland.
"The Ethiopian government is deeply saddened by the barbarous act committed against our innocent nationals," a government statement said.
Officials were working to identify the victims, it said.
Ethiopia will observe three days of national mourning starting on Tuesday, with flags lowered to half-staff mast to mourn what it described as "atrocities committed against our nationals in Libya and South Africa".
Ethiopian nationals have also been caught up in a wave of anti-immigrant violence sweeping across South African townships.