The Defence Ministry in London said three crew members were "all safe, with minor injuries".
A spokesman described "an emergency landing just north of Sarajevo at around 1800 GMT" on Monday.
But he rejected press reports that the craft, a British Lynx utility helicopter, was forced down, and declined to comment on its activity.
The crew and craft are part of a British contingent participating in the EU-led Stabilisation Force (SFOR), a peacekeeping mission first deployed after Bosnia-Herzegovina's 1992-95 war.
The European Union has a 7000-strong force at Camp Butmir in Sarajevo, and SFOR - now made up of 30 countries including 22 EU nations - is led by British General David Leakey.
Sarajevo, the capital of the Muslim-Croat Federation, and the Serb Republika Srpska, comprise post-war Bosnia.