The tournament starts on June 14 and is set to attract 2.7 million fans to stadiums and up to 12 million at public viewing events.
"For the Euros, we are pooling the forces of the security authorities even more strongly and preparing for possible threats," Interior Minister Nancy Faeser told the Rheinische Post newspaper.
"During the tournament, we will conduct temporary border controls at all German borders to prevent potentially violent actors from entering," she said.
The comments follow a mass shooting at a concert in Moscow, in which at least 139 people were killed and 180 injured. Western intelligence has linked the attack to the Islamic State militant group and France said it was raising its terror alert warning to the highest level following the attack.
Germany already has temporary controls at its borders with Poland, the Czech Republic, Austria and Switzerland, as part of efforts to combat migrant smuggling gangs.
These could be extended but no specific measures have been decided yet, an interior ministry spokesperson said on Monday when asked about security surrounding the European championship.
