That represents a doubling of such cases since January and is likely to deepen concerns about the threat level in Germany, which has not suffered a large-scale Islamist attack like those that have rocked neighbours France and Belgium in recent months.
In the past, the German government has played down the risks of Islamic State fighters entering Europe with the tide of migrants, in part to avoid exacerbating public concerns about the influx, which hit a record 1.1 million last year.
But the head of Germany's domestic intelligence agency Hans-Georg Maassen told a conference last week that although there were more efficient ways to smuggle in fighters, Islamic State appeared to have sent some via the Balkan route from Greece in order to fan fears about refugees and "send a political signal".
"I am not telling you a secret when I say that I am concerned about the high number of migrants whose identities we don't know because they had no papers when they entered the country," Maassen said.
The number of migrants entering Germany reached peaks of more than 10,000 a day last autumn, but has fallen dramatically in recent months due to the closing of the Greek border with Macedonia and a deal between the European Union and Turkey that has discouraged refugees from crossing the Aegean Sea.
The reduction in the numbers has eased pressure on German Chancellor Angela Merkel, who came under fierce criticism last year for welcoming hundreds of thousands of migrants fleeing war in the Middle East with the optimistic slogan "We can do this".
A spokeswoman for the Bundeskriminalamt (BKA), or federal police, said there had been 369 warnings about possible extremists entering the country since the influx of refugees accelerated last year, of which 40 merited further investigation by federal and state authorities.
That represents a sharp increase from the 213 warnings and 18 investigations that the police had recorded in early January.
"German security officials have indications that members and supporters of terrorist organisations are being smuggled in with refugees in a targeted, organised way in order to launch attacks in Germany," the BKA spokeswoman said, noting however that there was no definitive confirmation of this.
Two of the suicide bombers from the Nov. 13 attacks in Paris that killed 130 people came into Europe through the Balkan route and so did two men who authorities believe were meant to participate in those attacks but were delayed and arrested in a refugee centre in Salzburg in December.
There is also evidence that Saleh Abdeslam, believed to be the lone surviving suspect from the attacks, picked up three unidentified militants who entered Europe with the refugees in the southern German city of Ulm in October of last year.
In early February, German authorities arrested a 35-year-old Algerian man and his wife at a refugee centre in the town of Attendorn. The man, a suspected Islamic State member, reportedly posed as a Syrian when he entered Germany in the autumn of 2015.
Days later, a 32-year-old man was arrested in the city of Mainz who is suspected of having fought with the militant group in eastern Syria before travelling to Germany via Turkey.