Ground handlers at airports in Munich, Duesseldorf and Cologne also walked out. They are expected to return to their posts by early afternoon.
Deutsche Lufthansa, which operates a total of about 1,850 flights on a typical day, said it canceled about 400 of its flights planned for Tuesday, in line with its expectations.
Smaller peer Air Berlin said 23 flights out of the several hundred scheduled would not operate - more than the expected eight cancelations.
More strikes may follow soon.
The head of German services union Verdi, Frank Bsirske, had said on Monday that if warning strikes were not sufficient to get a pay deal moving, the union could take a tougher line in coming weeks.
If the union and employers fail to agree in talks this week, the dispute could go to mediation. Should mediation fail, the union could ballot its members on a broader strike in the second half of April, Bsirske had said.
Verdi is pushing for a 6.5 percent pay rise for around 2 million federal and local public-sector workers, and at least 200 euros more per month.
More then 50 percent of Fraport’s shares are held by the regional state of Hesse and the city of Frankfurt and its ground handlers have public-sector work contracts.
Employers have offered a 3.3 percent rise over a period of 24 months and a one-off payment.
