Torn-up sick notes were found in the homes of Andreas Lubitz, they say, including one for the day of the crash, which killed 150 passengers and crew.
The illness was not named, amid reports Mr Lubitz had mental health problems.
Lufthansa, which owns Germanwings, has announced new rules to ensure pilots are never left alone in the cockpit.
Data from the voice recorder suggests Mr Lubitz purposely started an eight-minute descent into the mountains while keeping the pilot locked out of the flight deck.
There were no survivors when Flight 4U 9525 crashed in a remote mountain valley on Tuesday while en route from Barcelona in Spain to Duesseldorf in Germany.
Internal aviation authority documents quoted by German media suggest the co-pilot suffered depression and required ongoing assessment.
Prosecutors say there was no evidence of a political or religious motive for his actions and no suicide note has been found.
Depression is more than just feeling a bit down for a few days. It is an illness which, at its most severe, can leave people feeling that life is no longer worth living. It can cause physical symptoms such as headaches, sleeplessness and constant tiredness which may last for months and months.
People with depression can also feel anxious, irritable and agitated on a daily basis but it affects everyone differently and only in rare cases is it a reason for violence against others.
If people admit their symptoms and talk to someone about their feelings, depression can usually be treated but the biggest barrier to getting help is often stigma and the fear of disclosing mental health problems.
In a (in German), prosecutors said they had seized medical documents from Mr Lubitz’s two residences – his Duesseldorf flat and his parents’ home north of Frankfurt – which indicated an “existing illness and appropriate medical treatment”.
The “fact that, among the documents found, there were sick notes – torn-up, current and for the day of the crash – leads to the provisional assessment that the deceased was hiding his illness from his employer”, the report states.
Sick notes from two different doctors were found, according to Germany’s Rheinischer Post newspaper.
Duesseldorf’s University Hospital told the paper Mr Lubitz had visited the hospital for “diagnostic clarifications” in February and, most recently, on 10 March.
Started training in 2008 at Bremen and in Arizona
Worked as co-pilot, or first officer, from 2013. Appeared pleased with his job
Lived in town of Montabaur, near Frankfurt, with his parents. Kept a flat in Duesseldorf
Pilot training was interrupted for some months in 2009 when, German media report, he suffered a depressive episode requiring treatment. He later passed all tests and was deemed fit to fly
According to German media, Mr Lubitz’s notes say he suffered a serious depressive episode when he finished training in 2009.
He reportedly went on to receive treatment for a year and a half and he was recommended regular psychological assessment.
Mr Lubitz’s employers confirmed his training had been interrupted for several months six years ago, without explaining why, but they insisted that he had only been allowed to resume training after his suitability was “re-established”.
Lufthansa announced it would adopt the “rule of two” as soon as possible, after other airlines swiftly moved to change their safety procedures.
“Under the new procedure, two authorised persons must be present in the cockpit at all times during a flight,” it said.
Recovery efforts are continuing at the crash site on the third day following the crash.
Investigators continue to comb the crash site for body parts, debris and the second “black box”, which records flight data.
Families are providing DNA samples to allow for identification of victims’ remains.
29 November 2013: A flight between Mozambique and Angola crashed in Namibia, killing 33 people. Initial investigation results suggested the accident was deliberately carried out by the captain shortly after the first officer (also known as the co-pilot) had left the flight deck.
31 October 1999: An EgyptAir Boeing 767 went into a rapid descent 30 minutes after taking off from New York, killing 217 people. An investigation suggested that the crash was caused deliberately by the relief first officer but the evidence was not conclusive.
19 December 1997: More than 100 people were killed when a Boeing 737 travelling from Indonesia to Singapore crashed. The pilot – suffering from “multiple work-related difficulties” – was suspected of switching off the flight recorders and intentionally putting the plane into a dive.