The International Committee of the Red Cross, whose headquarters was bombed on Monday, is also considering whether to scale back its operations in the city.
The withdrawal of MSF is a huge symbolic blow to US attempts to restore a semblance of normality to Baghdad and the rest of central Iraq. If the aid agencies judge central Iraq too dangerous to operate in, it will be even harder for Washington and London to persuade private companies to take up reconstruction contracts in the country.
Brendan Paddy, a spokesman for Save the Children Fund, said the MSF decision was "extraordinary because, like the ICRC, they are usually first in and last out". He said he understood why so many agencies were withdrawing or had withdrawn: "If you are spending all day hiding in a bunker, is there any point in being there?"
It continues to operate in the north and south of Iraq. Mr Paddy said the agency kept assessing the situation to see whether it could go back into central Iraq but "all the signs are that things getting worse rather than better".
Some of the aid organisations are reluctant to talk much about their continued presence in Iraq for fear of becoming the next target. One aid agency spokesman who opted for anonymity, said: "If the UN and the ICRC can be targeted, we could be next."
The biggest aid organisation of all in the country, Care, which has been in Iraq since 1991, is planning to stay. It has eight international staff in the country and 70 nationals and helps with water supply, sanitation and health.
Oxfam took a decision not to have international staff in the country after the UN bombing, but it still has 50 local staff.
Britain's Department of International Development said yesterday it also intended to stay. It has 25 staff working on a range of projects.
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