Turkey-led Syrian rebels have advanced steadily since launching a January 20 assault on Afrin, which is controlled by the Kurdish People's Protection Units (YPG). Nine terrorists were also neutralised in the operation dubbed Olive Branch.
According to the report, Turkish army shelled the battle area to allow the evacuation of wounded soldiers.
The attack reportedly happened in the Keltepe district as Kurdish fighters ambushed Turkish special forces by emerging from a tunnel, and a rescue helicopter sent to evacuate the wounded had to return after it was hit as well, reported a private news media outlet in Turkey.
Ankara views the YPG as the Syrian branch of the militant Kurdistan Workers' Party (PKK) that has been fighting for an autonomous region inside Turkey since 1984.
The Syrian government has already condemned the "brutal Turkish aggression" against Afrin, rejecting Ankara's claim about having informed Damascus of the operation.More news: NFL, Papa John's split; another Louisville-based company takes league deal
The total number of terrorists neutralised since the start of the operation has risen to 2,295, according to a tally by Anadolu Agency.
The main aim of the Turkish forces is to establish security and stability along Turkey's borders.
The Syrian Civil Defence said one person was killed.
The Russia-ordered pause came after a UN Security Council resolution calling for a nationwide 30-day ceasefire failed to take hold.
The military has also said that only terrorist targets are being destroyed and "utmost care" is being taken to avoid harming any civilians.
Afrin has been a major hideout for the YPG since July 2012, when the Bashar al Assad's Syrian regime left the city to the group without a fight.