Thousands of police officers were on Monday patrolling central Athens which will be closed to traffic for several hours on Tuesday while Obama holds talks with Greek Prime Minister Alexis Tsipras and President Prokopis Pavlopoulos.
Security measures have been beefed up "as the circumstances require," a police source told AFP.
Obama was set to leave Washington later Monday to embark on his last trip to Europe as president before he hands over to Donald Trump in January.
He will be in Athens on Tuesday and Wednesday, with Greece's economic woes and Europe's migration crisis high on the agenda.
Greek trade unions, leftist and anarchist parties had called for protests in Athens on Tuesday to denounce "imperialist" US involvement in wars in the Middle East.
"During the two days of Obama's visit, protests and assemblies are banned for security and public order reasons," police said in a statement Monday.
The boosted police measures also come after unknown assailants threw a grenade at the French embassy in Athens last week, slightly wounding an officer on duty.
Police blamed anarchists for the attack.