A bomb near a road is thought to have been involved and a military spokesman said one of the other soldiers was "possibly seriously" injured.
It happened north of the UK battle group's base at Camp Dogwood, 20 miles (32km) from Baghdad.
On Sunday, two other Black Watch troops were injured by a suicide car bomb and three died in an attack on Thursday.
Two of the soldiers injured in the attack on Sunday have been flown to Germany to get medical treatment.
"As the prime minister said this afternoon, we salute their dedication, professionalism and sheer courage."
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