The suspect was taken into custody after the incident just before 1.30pm in Hamilton Road, Golders Green, north-west London, which has a large Jewish population.
Video shared on social media appears to show a man brandishing a large knife as shop staff attempt to fight him off with a trolley.
He then moves towards the shop before walking away from the scene.
A suspect was later arrested on suspicion of possession of an offensive weapon, criminal damage and racially aggravated affray.
Nobody was hurt and a knife was recovered from the scene, the Metropolitan Police said.
The incident is not being treated as terror-related, the force added.
The CST charity, which says it helps Jews with “security and antisemitism”, said: “CST is aware of an incident involving a man with a knife shouting antisemitic abuse at a kosher shop in Golders Green, north London.
“Police were called and arrested the suspect. Nobody was harmed and the incident is now over.”
Inspector Scott Barden-Marshall, from the local policing team in north-west London, said: “I know this incident will cause concern in the community.
“Officers responded quickly and made an arrest within 10 minutes.
“An investigation is now under way to establish the circumstances.”