Kuwait's state news agency KUNA said two of the injured were Lebanese employees of the information office, which is affiliated with the Kuwaiti embassy in Lebanon.
The third person has not yet been identified.
The cause of the blast was a hand grenade, KUNA said.
But a security source said the explosion appeared to be caused by a booby-trapped package delivered to the office.
The blast, which occurred on the 10th floor of a building in the shopping district of Hamra, was the latest in a string of bombings to hit the Lebanese capital this year.
Security forces cordoned off the area leading to the scene
"The criminal investigation brigade is probing the exact cause of the explosion which was either due to a booby-trapped package or letter," a Lebanese army officer said.