After the defeat of Germany in World War II, an estimated 2.5 million Germans were driven out of the Sudetenland in the western part of what was then Czechoslovakia and their property confiscated.
The area had been annexed by Germany in 1938.
"The (German) government will not support the individual demands for compensation in connection with the Second World War in national or international courts," Schröder told the Czech newspaper Hospodarske Noviny Monday, referring to similar claims by Germans who were expelled from Poland after 1945.
"That naturally also applies to the Czech Republic," Schröder said in an interview.
During his visit Schröder also met with the Czech Republic's new prime minister Stanislav Gross.
Dozens of Sudeten Germans are seeking to take their case for compensation to the European Court of Human Rights in Strasbourg.
Polish-German legal defense council
Their initiative mirrors the campaign to win damages being mounted by some Germans expelled from territories in eastern Germany that became Polish after 1945. The German and Polish governments have recently set up a common legal defense council to fight off any compensation claims from citizens of either country.
"In common with (Polish) Prime Minister Marek Belka, we have confirmed the common attitude of the German and Polish governments that there is no longer any room for claims for restitution coming from Germany," Schröder told the newspaper. "We do not want to burden our relationship with political and legal questions dating from the past, we want to point them to the future."
Schröder said the Sudeten Germans' claims were "devoid of any legal basis."
In 1997, after months of difficult negotiations, Germany and the Czech Republic signed a joint declaration mutually recognizing past mistakes and undertaking to open a new chapter in their relationship.