German justice minister Sabine Leutheusser-Schnarrenberger wrote to her British counterpart Chris Grayling and Home Secretary Theresa May questioning the legal basis for the programme code-named Project Tempora.
In her letter she questions whether the collection of data, which is held for up to 30 days, is triggered by "concrete suspicions" or part of a general trawl.
Ms Leutheusser-Schnarrenberger also warned that she will raise the issue at next month's meeting of EU justice and home affairs ministers in Brussels
The Ministry of Justice confirmed it had received her letter and would respond "in due course", while a Home Office spokesman said: "We do not routinely comment on private correspondence."
Precisely how US fugitive Edward Snowden got out of Hong Kong remains a mystery, but many here in China are hailing him as a hero.
Edward Snowden is believed to be in Moscow and was not on a flight to Havana earlier as expected.
Whatever you think of Edward Snowden, he's changed the way the world's two largest powers deal with each other.