The Munich paper, citing a document which outlined a series of measures approved in Berlin Friday, reported that the new programme will come into effect by the end of May. Berlin's lower house of parliament, the Bundestag, must still approve the new tests.
Carsten Spohr, head of German air giant Lufthansa, which owns low-cost subsidiary Germanwings, already announced in May 2015 surprise medical checks for the company's pilots.
Spohr's announcement came shortly after the March 24th Germanwings crash, when all 150 people on board a jet travelling from Barcelona to Duesseldorf were killed after 27-year-old Andreas Lubitz crashed the plane into the Alps.
After the crash, it was revealed that Lubitz suffered from depression, and that the airline knew about his health condition.
The disaster raised serious questions about Germany's balance between privacy protections and public safety, as many wondered if the company could have done more to prevent the crash.
The document cited by the paper Saturday said airlines must ensure that only employees in a state to ensure "a safe and controlled" journey would be allowed to fly.
The tests would make sure that pilots are not "under the influence of medication, alcohol or other psychoactive drugs," when there is a doubt about their abilities.
In July 2015, the European Aviation Safety Agency (EASA) recommended more medical testing for pilots, including more psychological tests.
The EASA also said that two people should always be in the cockpit, a rule not yet imposed by the EU.