Staff at the embassy in Baghdad and the consulate in Irbil must leave as soon as possible on commercial transport.
Germany has meanwhile suspended its training of soldiers in Iraq.
The US military said on Tuesday that the threat level in the Middle East had been raised in response to intelligence about Iran-backed forces in the region.
It contradicted a British general who had said there was no increased threat.
Chris Ghika, deputy commander of the global coalition against the Islamic State group, told reporters that measures in place to protect US forces and their allies from Iran-backed militias in Iraq and Syria were “completely satisfactory”.
“We are aware of their presence clearly and we monitor them along with a whole range of others because that is the environment we are in,” he added.
But a spokesman for the US military’s Central Command later disputed Gen Ghika’s comments, saying they ran “counter” to the credible threats identified by US and allied intelligence agencies.
Central Command, in co-ordination with the global coalition’s Operation Inherent Resolve (OIR), had “increased the force posture level for all service members assigned to OIR in Iraq and Syria”, Capt Bill Urban said in a statement.
“As a result OIR is now at a high level of alert as we continue to closely monitor…