SOS Chretiens d’Orient (Christians of the Middle East) said the three French nationals and one Iraqi were last seen in Baghdad on Monday.
The charity said there had been no ransom demands.
Their disappearance comes at a time of heightened tensions in the country.
A top Iranian general and Iraqi militia commander were killed in Baghdad earlier this month in a US drone strike. Lawmakers and protesters have responded by calling for foreign troops to leave.
SOS Chretiens d’Orient said its four employees were primarily in Baghdad to complete “administrative formalities”, such as renewing their visas and registering the organisation with authorities.
The charity described the four as “experienced employees, in good health and with perfect knowledge of crisis zones”. Their identities have not been disclosed.
SOS Chretiens d’Orient says it seeks to help Christians in the Middle East and has been working in Iraq since 2014.
An official at the French Foreign Ministry told Reuters news agency it was aware of the situation and was trying to secure more information.