Since September, more than 300 houses, including four churches, have been burned to the ground in the now deserted town.
Spokesman for the Zamfara State police, DSP Mohammed Shehu, confirmed the threat to Sahara reporters.
After spending about four to five hours in custody, Bukovinac and the other pro-life activists were released.
The Chinese Christian minority faces regular persecution from the Communist authorities.
The Ethiopian government closely monitors international cooperation organisations, including those linked to the Catholic Church
Kayah State is a stronghold of Catholicism, with a population of 90,000 Catholics, about one-quarter of the total population.
ICC has recently paid hospital bills to 10 victims within the district, as well as some from other communities.