The staff of the Al-Forat security company were "arrested as they planned to carry out terrorist activities against innocent people", the ministry said in a statement on Monday.
The 31 employees were picked up from the central Hamra hotel, which houses the offices of a number of foreign firms, including media organisations, the ministry said without specifying the day of the arrests.
Bayan Jabr Solagh, the Iraqi interior minister, said Al-Forat "does not have a licence from our ministry" to operate as a security firm and charged that some of its detained employees had confessed to participating in violence.
 "We discovered a lot of weapons including sophisticated rifles usually used by snipers, and also rocket-propelled grenades," the minister told state television.
"I am astonished how a private security company can have arms like RPGs as our ministry does not allow such companies to have more  than revolvers and Kalashnikovs."