Another man was badly injured in the shooting, the ministry’s Public Security Department said in a statement.
Several others were being treated after they suffered from suffocation.
The shooter is still alive while an investigation is underway, it added.
Al-Ghad newspaper reported that the incident took place at the Italian hospital in al-Karak, where the shooter works at the laboratory.
Al-Karak province is located around 130 kilometres south of the Jordanian capital Amman.