"In view of the security situation, the foreign ministry advises against all unnecessary travel to Syria until further notice," the ministry said in a statement.
The ministry also urged travelers in Syria to avoid demonstrations and large crowds. In addition, "travelers should avoid being in or near larger mosques around the time of Friday prayers".
Denmark also said it would halt all deportations of Syrians who have been denied asylum back to Syria because of the security situation.
"The Refugee Appeals Board has decided, following an inquiry by the foreign ministry, to suspend all forced deportations to Syria until further notice," the board said Thursday.
Syria has been gripped since mid-March by deadly protests calling on the regime of President Bashar al-Assad, in power since 2000, to introduce sweeping political reforms.
Demonstrations spread to Syria's second city Aleppo on Thursday following a weekend of confrontation between security forces and activists during which 30civilians were killed, according to rights activists.