Insurgents attacked the British soldiers in the southern province of Helmand at 4pm (1130 GMT) on Friday, according to statements from Nato and the British ministry of defence.
One insurgent was killed in the fighting. The wounded soldier was evacuated for medical treatment.
Britain has nearly 4,000 soldiers deployed in Helmand as part of a Nato-led security force battling to bring security to turbulent southern Afghanistan.
Twenty-two British soldiers have died in the country since November 2001, 17 since this March when it moved into Helmand, also the hub of Afghanistan's world-leading heroin industry.
The province has seen the worst of the recent fighting, during the biggest upsurge in violence in nearly five years since the ouster of the Taliban government by US-led forces.
Taliban insurgents have stepped up attacks, rendering much of the south and east of the country a no-go zone for civilians. Insecurity has also spread to new provinces, such as Ghazni, where Taliban-led fighters are more active than in the past.
On Friday, suspected Taliban ambushed the chief of the central province's Muqur district, Habibullah Jan, as he travelled by car to the provincial capital, Abdul Ali Faqari, the Ghazni governor's spokesman, said. Four of his bodyguards were wounded in the attack.
In the east, a homemade bomb believed planted by Muslim fighters badly damaged a newly built co-ed school in Paktika province on Friday, a US-led multinational force statement said.
At the time, no one was inside the school, which was due to open next week.
Taliban insurgents have attacked scores of schools in an effort to undermine the already weak government of Hamid Karzai, the president. The attacks also appear motivated by ideological opposition to girls' education.
Meanwhile in the north, German military police arrested seven suspected insurgents from a 4WD vehicle that subsequently exploded near the entrance of a military compound in the city of Mazar-e-Sharif on Friday, a Nato statement said. No one was hurt.