Out of nearly 1,800 planned flights on Monday, "we will operate 20 short and medium-range flights and 12 long-distance services," a spokesman told AFP.
At Lufthansa's main hub in Frankfurt, Germany's biggest and Europe's third-biggest airport, just six out of a total 50 flights would go ahead, and three from 17 at Munich.
Services union Verdi called the strike after three rounds of pay talks with management ended without any agreement.
Verdi is demanding a 5.2-percent pay increase for 33,000 Lufthansa ground staff, plus employees of various subsidiaries as well as cabin crew members who are Verdi members.
The escalating pay dispute threatens to cause transport chaos across Europe's top economy and comes a month after Lufthansa was forced to cancel nearly 700 out of a total 1,800 flights due to half a day of warning strikes.
Lufthansa board member Stefan Lauer, said the action, described as a 24-hour warning strike, was "de facto an all-out strike" that was "a completely excessive measure that can in no way be justified in view of the current state of negotiations."
Verdi has accused management of "playing with employees' fears about their future and their jobs" in refusing to make any concrete guarantees.
The union has complained that the offer tabled by management represented an increase of 0.4-0.6 percent over a period of 12 months.