According to News.com.au the woman fled the scene which forced the school to declare a lockdown.
She was later arrested at her home on Beach Side Drive, Suffolk Park about 10.30am and lockdown was lifted shortly afterwards.
NSW Police issued a statement about the assault, saying: "Police will allege a 28-year-old man and a 36-year-old woman were speaking on the premises before she approached him with what's believed to be a pair of scissors."
Police are in the process of interviewing the alleged attacker and charges are expected to be laid later today.
Parents and members of the Byron Bay community took to Facebook to share their outrage at the news, with one claiming school children saw "a pool of blood" near the library.
Another person described the teacher involved as "most lovely and so undeserving" of the attack.