A spokesman for Berlin prosecutors confirmed to Bild that Beck had been arrested on Tuesday at around 11pm in possession of 0.6 grammes of a controlled substance.
The tabloid further reported that the drug was methamphetamine, otherwise known as crystal meth, although other German media have yet to confirm that.
Beck, who until Wednesday was the Green party's domestic policy spokesman, behaved "co-operatively", the tabloid reported, quoting anonymous police sources.
"I hereby make available my offices as domestic and religious policy spokesman of my parliamentary group and as chairman of the German-Israeli parliamentary friendship group," Beck told Bild.
"I have always argued for a liberal drugs policy," he added. "My lawyer will give a statement to prosecutors at the appropriate time. I will not comment publicly."
Politicians and commentators were quick to react online.
"If you make your offices available then you're saying to the group that you could take them up again, if they wanted you to," Berlin state parliamentarian Christopher Lauer wrote.
Stellt man seine Ämter zur Verfügung, sagt man der Fraktion, dass sie die Ämter neu besetzen kann, _wenn_ sie das möchte.- Christopher Lauer (@Schmidtlepp) March 2, 2016
"Volker Beck is supposed to have had a "substance suspected of being a narcotic" on him. Maybe it was an essay by [Green parliamentary leader] Anton Hofreiter," quipped TV journalist Hajo Schuhmacher.
Volker Beck soll eine "betäubungsmittelsuspekte Substanz" bei sich geführt haben. Vielleicht war´s ein Aufsatz von Anton Hofreiter.- hajo schumacher (@hajoschumacher) March 2, 2016
"What a shame, Volker Beck gives up his offices. There could have been other reasons for that," Frankfurter Allgemeine Zeitung journalist Philip Plickert wrote, including a link to an article about the politician's support for decriminalizing paedophilia in the 1980s.
"If you look at the rancour here, Volker Beck must have done a bunch of things right up to now," Tom Strohschneider, editor of left-wing weekly Neues Deutschland wrote.
Wenn man sich diese Häme hier anschaut, muss der @Volker_Beck bisher ne Menge richtig gemacht haben.- Tom Strohschneider (@Linksdings) March 2, 2016
While the Green party has long argued for a more liberal drugs policy that would not criminalize users, it has more often been in the headlines for its pro-legalization stance on cannabis than harder substances.
Party co-chair Cem Özdemir was filmed with a cannabis plant for his contribution to the "ice bucket challenge" social media craze in 2014, although he later denied that the plant belonged to him.