Vertonghen's wife and children were held by four men wearing balaclavas and wielding machetes, who then made off with electrical items.
The family was physically unharmed during the incident, which took place last week when the Belgium centre-back was part of the Spurs squad beaten 3-0 at RB Leipzig.
"I'm okay. Obviously it's a big shock for everyone," Vertonghen told The Sun. "The family are in shock but okay. It is what it is."
A statement issued by the Metropolitan Police read: "Police were called to a residential address in NW3, at 19.49hrs on Tuesday, 10 March to a report of a burglary. Officers attended.
"It was reported four men wearing balaclavas, armed with knives, had entered the property and stolen a number of items before leaving.
"Nobody was injured. The suspects had left the scene before officers arrived.
"There have been no arrests. Enquiries continue."
Both the police and Tottenham have urged anyone with information that could assist with the enquiry to call 101 and give the reference CAD 7358/10Mar.