Airports in Düsseldorf, Nuremberg and Dortmund said they were affected, while at least two others were reported to have been hit.
German news outlet Der Spiegel said a group of Russian hackers had claimed responsibility for the attack, although there was no comment from authorities about who was behind it.
The sites were believed to have been targeted by so-called "distributed denial-of-service" attacks, designed to overwhelm the target with a flood of internet traffic, preventing the system from functioning normally.
"The site is being overwhelmed by massive demand," said a spokesman for Nuremberg airport, adding that it was "uncertain" when it would be back to normal.
READ ALSO: EXPLAINED: How Germany is preparing to ward off future cyberattacks
Germany has been on high alert for Russian cyberattacks since Moscow invaded Ukraine.
Last month, the websites of airports, public administration bodies and financial sector organisations were hit by cyberattacks that authorities said were instigated by a Russian hacking group.
The Federal Office for Information Security said in October the threat level for hacking attacks and other cybercrime activities was higher "than ever".
On Wednesday, German airline giant Lufthansa was forced to cancel or delay flights due to a major IT outage caused by construction work in Frankfurt, the location of its main hub.
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