A police patrol discovered the damage at the Jewish delicatessen and kosher store at Lyngbyvej in Østerbro at 3.30am on Thursday, according to the Berlingske Tidende (BT) newspaper.
One of the shop's windows was partly broken and the word “Jødesvin” (Jewish pigs) was scrawled on a wall, BT reports.
After the Copenhagen shootings on February 14th, Danish police have kept a close eye on Jewish institutions and stores, including the delicatessen on Jagtvej.
“All vandalism is serious, but it is obvious that when it comes to this particular location, there will be an extra focus on it,” police investigator Kenneth Jensen told Berlingske.
Police believe a stone was thrown through the window. Investigators were examining surveillance footage on Thursday, as well as conducting a search inside the store.
After the Charlie Hebdo terror attack in Paris in January, the Danish government started reviewing its anti-terrorism strategies.
This resulted in the publication of a 12-point plan, which was published after the Copenhagen shootings.
This includes a proposed increase in the budget for the protection of Jewish institutions.
The anti-terror plan covers a four-year period and is expected to cost close to one billion kroner (€134 million).
The government and opposition have however not yet agreed on how to finance the full package but the government has told the police they will be allocated an extra 20 million kroner for the protection of Jewish institutions in 2015.
February's attacks saw Omar El-Hussein, a Danish-born man of Palestinian origin, killed in a shootout with police after he opened fire at a cultural centre, killing filmmaker Finn Nørgaard, after which he shot dead Dan Uzan, a Jewish guard outside the city's main synagogue.