The sparse response by the British government, seen by the German Press Agency DPA, advised Germany to address its concerns directly to the intelligence services.
Germany has demanded answers from Britain over its Tempora electronic surveillance programme, warning that measures "shrouded in secrecy" harmed democracy, and urging that the controversy be dealt with at EU level.
"Questions have been raised concerning the extent to which especially German citizens have been targeted," she wrote to her British counterpart Christopher Grayling and to the Home Secretary, Theresa May.
Charges that Britain's intelligence services are tapping cables that carry the world's phone calls and internet traffic came from documents leaked by US ex-intelligence technician Edward Snowden, who remained holed up at Moscow airport and is wanted on spy charges in the United States.
Leutheusser-Schnarrenberger asked about reports that "the British Tempora project enables it to intercept, to collect and to store vast quantities of global email messages, Facebook posts, Internet histories and calls for 30 days" and that these were being shared with the US intelligence agency NSA.
She asked Britain to clarify whether data is retained "without any concrete evidence of any wrongdoing, whether judges have to authorize measures of this kind, how their application works in practice, which data are stored and whether German citizens are covered by measures of this kind."
She stressed that "the transparency of government action is of key significance in any democratic state and is a prerequisite for the rule of law.
"Parliamentary and judicial scrutiny are central features of a free and democratic state but cannot come to fruition if government measures are shrouded in secrecy."
Germany is especially sensitive over privacy and data protection, given its dark history of state surveillance and secret police abuses under the Nazis and the communist East German regime.
The minister last weekend said the Tempora accusations would be a "catastrophe" if true and added: "The allegations against Great Britain sound like a nightmare out of Hollywood ... European institutions should shed light on this immediately."
In her letters to the British government, she again stressed that "these measures must be raised in an EU context" at ministerial level and as part of ongoing discussions on the EU Data Protection Regulation.