The president also drew parallels between masked protesters and the Islamic State group - prompting organisers of the recent rally to say her comments had left them "speechless".
More than 60,000 people protested against the conservative government's push for labour reform and state-issued history textbooks in Seoul on November 14, in the biggest protest in the country for nearly a decade.
Many scuffled with police, who responded with water cannon and liquid pepper spray, leaving dozens injured and one protester in a critical condition.
Park described the clashes on November 14 as an "unacceptable" incident and called for "strong measures" against the protesters, especially those in masks.
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"At a time when acts of terrorism are taking many lives around the world, some terrorist elements may sneak into such protests and pose a threat to the lives of our people," she said at a cabinet meeting today.
"In particular, masks in protests should not be tolerated. Isn't that what the IS is doing these days, with their faces hidden like that?" she added, referring to the Islamic State jihadi group.
"This is really pathetic," KCTU said in a statement.
"We never expected her to have any insight in democracy but now we are left to wonder if she has any sense of judgment."
KCTU added: "Her statements over IS and masks ... Left us simply speechless."
The November 14 demonstration saw police surround demonstrators with barricades composed of hundreds of police buses, with protesters - some wearing masks - tying ropes to the vehicles to try to move them.
The protest focused on a series of issues, including Seoul's planned labour reform critics said would make it easier for firms to fire workers, and the controversial imposition of state-issued history textbooks in schools.
The textbooks have become a bitter ideological battleground between left and rights.
The organisers of the November 14 rally have vowed to launch another massive protest on December 5.