Thousands of students formed human chains outside schools as they continued to push the government to meet their five demands despite last week's pledge to withdraw the extradition bill, the South China Morning Post reported.
The knife attack took place outside Cognitio College in Kowloon when the man injured the teacher who was trying to protect students who formed a human chain.
A video circulating online showed the agitated, shirtless man in blue shorts, waving a box-cutter at people dressed in black, with some onlookers trying to calm him.
A police spokesman said the teacher suffered hand injuries and was taken to Queen Elizabeth Hospital.
The man left before officers arrived and is currently on the run, the spokesman added.
A school representative said no students were hurt in the attack.
In another incident at the PLK Vicwood KT Chong Sixth Form College, Tai Kok Tsui, a human chain was disrupted when an alumnus was injured by a falling object, according to authorities.
It was unclear where the object came from.
Students from more than 120 schools across the city took part in the collective action on Monday.
Most students opted to form human chains before class started at about 8 a.m., rather than join the boycotts.
( With inputs from IANS )