The Taliban claimed the attack which Kandahar provincial governor spokesman Fazal Bari Baryalai told AFP "totally destroyed" one of the vehicles carrying Romanian soldiers in Daman district.
A spokesman for NATO´s Resolute Support train and assist mission confirmed a "small number" of soldiers were wounded.
In a WhatsApp message to journalists, Taliban spokesman Qari Yousuf Ahmadi said "seven invading forces" were killed. The militants routinely exaggerate battlefield claims.
Provincial police chief General Abdul Raziq told AFP the scene had been cordoned off by foreign forces.
The Taliban´s latest assault follows the militant group's pledge to turn Afghanistan into a "graveyard" for foreign forces after US President Donald Trump´s announcement to keep American boots on the ground indefinitely.
Earlier this month two Taliban suicide bombers launched separate attacks around Bagram Airfield, America´s largest base in the country, that wounded several US soldiers and civilians.
One of those attacks was in direct response to a US leaflet drop in the northern province of Parwan, where Bagram is located, that offended many Muslims in the deeply religious country.