Army military spokesman Lt Gen Qassim al-Moussawi said Gov Ahmed al-Dulaimi was wounded today during clashes near Haditha.
The US said today its forces launched airstrikes at the Haditha Dam to stop Islamic State militants from capturing it.
Al-Moussawi did not elaborate on al-Dulaimi's condition. Anbar long has been a contested region between Iraqi forces and Islamic State militants backed by allied Sunni tribes.
The situation deteriorated significantly in late December, and the militants took over parts of the provincial capital of Ramadi and the city of Fallujah.