Al Asad air base and a site in Erbil were both attacked, with a total of 15 missiles being fired - ten hitting Al Asad and one striking the base in Erbil.
A Pentagon spokesman said those personnel were diagnosed with concussion and traumatic brain injuries (TBIs).
Earlier this month, the US put the number of injured soldiers at Al Asad at 11, after previously insisting there had been no casualties.
The UK's Ministry of Defence now says none of its personnel were present at the site during the time of the attack, although British troops are thought to have been in Erbil.
Eight of the 34 troops who were transported to Germany are now in the United States, after arriving yesterday morning.
Nine personnel remain in Germany undergoing evaluations and treatment.
One service member who was taken to Kuwait has now returned to Iraq, while 16 diagnosed with concussions and TBIs remained in Iraq and have since returned to duty.
Al Asad air base, which is 100 miles west of the Iraqi capital Baghdad, is a key base for the US-led coalition in the country, of which the UK is a member.
Around 1,500 American military personnel are based there, as well as hundreds more from other coalition nations.
The US has more than 5,000 troops in Iraq.
The UK has around 400 non-combat personnel in the country as part of a US-led coalition, training the Iraqi and Kurdish Security forces to fight so-called Islamic State (IS).
The US-led coalition's training mission of Iraqi forces in the country had already been suspended prior to the attacks on military bases at Al Asad and in Erbil, including the UK's role.
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