The device exploded in a post room at the site in Zagreb at around 6.30am BST, but a spokesman claimed the male employee had only "very minor" injuries.
Security has been stepped up at the site as a result of the blast, but embassy officials could not confirm if a specific threat had been received.
Ambassador Sir John Ramsden has gone to the scene as a joint investigation with local police is carried out.
Eyewitnesses said there was no visible damage to the embassy building, in a commercial area on the edge of downtown Zagreb.
Croatian policemen were this morning guarding the site and sniffer dogs were used as officers carried out searches of the premises.
A FCO spokeswoman said: "One person suffered minor injuries when an explosive device detonated in a post room.
"Their injuries are not thought to be life-threatening and an inquiry is under way."
In May, two home-made hand grenades were hurled at a building housing the British Consulate in New York, causing minor damage.
Officials there could not be clear whether the consulate itself had been targeted, but the strike came on the day of Britain's General Election.