The minister said the German government will try to clarify how the alleged spying occurred, Reuters reported.
The accusations arose after the German newsmagazine Der Spiegel gave the government evidence that the U.S. National Security Agency had monitored Merkel's mobile phone for more than 10 years.
"If we find culprits and if we can identify them, they must live with the legal consequences, and if they are diplomats, they must leave the country," Friedrich said Monday.
"I am of course disappointed that an intelligence service, which elsewhere co-operates closely with us in the fight against terror, thinks they have the right to monitor the chancellor. That is something we can not accept."
U.S. Secretary of State John Kerry flew to Rome and Paris on Saturday and faced outrage over the sweep and scope of U.S. snooping abroad.
Still, parties on all sides acknowledge that spy-versus-spy eavesdropping is widespread even among allies.
"The magnitude of the eavesdropping is what shocked us," former French Foreign Minister Bernard Kouchner said in a radio interview.
"Let's be honest, we eavesdrop too. Everyone is listening to everyone else. But we don't have the same means as the United States, which makes us jealous."