The lawsuit asks a federal judge to rescind the pay freeze recently announced by Quinn.
On Thursday, the union announced it had sought an arbitrator's ruling on Quinn's decision last week to ditch $75 million in raises for 30,000 workers to help deal with the state's budget crisis.
Quinn spokesman Grant Klinzman's reaction to the lawsuit was only to say the Chicago Democrat's administration will take "the necessary steps to manage the fiscal year 2012 budget." Quinn had said he was "happy to go to the arbitrator."