The cancellations are expected to create massive problems for passengers in Germany and around Europe, as the company said it would fly only 32 routes for the day.
The airline also canceled long-distance flights that might have begun Sunday but weren't landing in Germany until Monday, The Wall Street Journal reported.
Members of the ver.di union have been seeking a 5.2 percent wage hike over the course of a year for 33,000 ground crew workers.
The company countered with an offer of a 2.3 percent wage increase for maintenance workers, 2.1 percent for baggage handlers and 1.7 percent for staff of Lufthansa, the newspaper said.
Included in the offer was a one-time bonus that would come to 1 percent of a worker's salary that would be available if the company reached an operating-margin target of 3 percent in 2014 and a $522 cash bonus for staff members.
The union called the offer "deplorable."
Last month, the company said its cost-cutting plan would add $966.2 million to its 2013 operating profit.