It is understood four men armed with knives made their way into his north-west London home and held his wife and children before making off with personal possessions.
The 50-year-old pundit, who has been working for ITV at the World Cup, tweeted on Wednesday night: "You won't get away with it."
A Scotland Yard spokesman said: "We are investigating an aggravated burglary at an address in north-west London after we were called at 9.20 last night.
"Personal possessions were stolen. The suspects are described as four black men aged between 18 and 25, with London accents, wearing dark clothing and hoodies obscuring their faces."
The Sun reported that the former Arsenal striker dashed back from the World Cup after learning the gang had held a blade to his wife Nancy's throat.
Wright's manager Steve Kutner said: "It was a terrifying ordeal. They marched Ian's wife from room to room.
"I would like to thank ITV for helping Ian to get home as quickly as possible."
Nancy, 39, is thought to have been put in a bedroom while the couple's two girls were taken to another room.