Police said the two, an Australian and a British citizen, were working for a Norwegian aid agency conducting a survey on unexploded ordnance.
The agency has named them as Trent Lee and Stephen Atkinson.
Inspector Clifford Tunuki said police were working overnight to clear the site of the explosion, which took place in a residential area in west Honiara.
Investigators will try to determine why explosives were present at a block of residential flats, which also serve as the project office.
The project aims to locate unexploded bombs dating back to the Second World War.