The action - which had been scheduled to run for four days - was called off after less than 24 hours of delays and cancellations for passengers.
The pilots had walked out at Lufthansa, Lufthansa Cargo and Germanwings over job security and pay issues.
There will be no further action until at least March 9, the union said.
A spokesman for the Cockpit union added the two sides had reached an agreement after a two-hour long hearing at a Frankfurt industrial court.
However the strike has already disrupted an estimated 10,000 passengers around the world, with the carrier trying to arrange alternative travel for them.
It had been offering train journeys to domestic air travellers, and attempting to rebook international passengers on other airlines.
The airline normally offers about 1,800 flights daily - of which 160 are long-haul trips.
A Lufthansa spokeswoman said that about 960 flights had managed to go ahead.
The strike will be officially lifted at midnight on Monday (2300GMT) - but it is not clear when services will return to normal.
Lufthansa's earlier offer of negotiations with the pilots was not initially taken up on Sunday before the strike began.
Frankfurt airport passengers
'If we crash, the whole company goes down'
Earlier a Lufthansa spokeswoman told the Associated Press that an injunction had been filed in Frankfurt, saying the action was "disproportionate".
German Transport Minister Peter Ramsauer had warned that the strike would hurt the country's economy as well as Lufthansa's reputation.
The airline - one of the world's largest - feared the action could cost it about 25m euros (£21.9m; $34m) per day.
The Cockpit union had arranged the action amid concerns the airline was increasingly relying on foreign pilots who fly for less pay.
It is worried that the company could try to cut staff costs by shifting jobs to foreign subsidiaries such as Austrian Airlines or Lufthansa Italia, where wages are lower.
The starting salary for a first officer in a Lufthansa cockpit is 62,000 euros, and 115,000 euros for a captain, according to the company's recruiting website.
Media reports say pilots' salaries can rise up to about 325,000 euros.
Cockpit has called for a 6.4% pay rise for pilots, more say in company decisions and commitments that pilots would keep their jobs when Lufthansa moves passengers to cheaper foreign affiliates.
But Andreas Bartels from the airline told the BBC the pilots' fear that their jobs would be outsourced was unfounded.
"That's what they fear but that's not reality. If you look to the reality, it's nothing like replacing or transferring jobs to other companies or other airlines [in] the Lufthansa airline system," he said.
Like most other global airlines, Lufthansa has struggled in the downturn. Sales slumped 13% in the first nine months of 2009.
As well as suffering from the more recent drop in consumer demand, the airline has also been facing the long-running threats posed by low-cost airlines and high fuel costs.
The UK's flagship carrier British Airways has also been locked in a dispute with cabin crew over pay and changes to working conditions.
Members of the Unite union voted overwhelmingly on Monday to take action - but did not immediately announce strike dates saying they hoped to negotiate with BA
In France, air traffic controllers are planning a four-day strike at Paris' Charles de Gaulle and Orly airports.
Unions have called for the strike from Tuesday to Friday in protest at plans to integrate European air traffic control, fearing it would lead to a loss of French jobs and civil servant benefits.
- Founded 1926
- Passengers: 76.5 million in 2009
- Flights: 893,200 in 2009
- Net loss: 32m euros in Jan-Sep 2009
- Employees: 118,945 as of Sep 2009