Assad is "the organiser and manager of the repression against the demonstrators," the Swiss economy ministry said in a statement announcing the asset freeze.
On May 18, Switzerland imposed an embargo on arms and equipment that could be used for internal repression.
The new measures expand from 13 to 23 a list of key players in the Damascus regime under financial sanction and travel restriction.
The list, which includes Assad, also targets intelligence chief Ali Mamlouk, interior minister Mohammad Ibrahim Al-Chaar, and head of political security Mohammed Dib Zeitoun for "involvement in the repression against demonstrators."
Top army commander Maher Al-Assad is identified as "the strong man of the Republican Guard" and "the principal manager of the repression."
Switzerland imposed these "restrictive measures ... due to the repression that the army and the Syrian security forces have exercised for nearly two months to stifle the peaceful demonstrations of the people."
At least 1,062 people have been killed by Syrian state security since the outbreak in mid-March of demonstrations against the Assad regime, according to Ammar Qurabi, president of Syria's National Organisation for Human Rights.
Qurabi also estimates that 10,000 people have been detained in the fierce government crackdown.
On Monday, the European Union tightened its own sanctions against Assad, blaming him for "unacceptable violence" directed against civilians.