Regulators have given LAN until the end of the week to leave.
The airline claims that the government wants to undermine the company's competition against state-owned Aerolineas.
Aviation trade unions say more than 1,000 LAN workers could lose their jobs in the eviction.
The Apta and ATCPEA unions represent technicians, flight attendants and ground crews.
"We've determined a nationwide stoppage for all airlines that operate out of Aeroparque - Aerolineas Argentinas, LAN, Andes and Sol," warned Apta leader Ricardo Cirielli.
Flag-waving union members blocked the road leading to Aeroparque on Monday and LAN went to court to try to block the regulator's decision.