Items of “significant value and of huge personal and sentimental importance to the family” were taken – thought to be jewelry and cash worth £100,000.
Club joint chairman David Sullivan said: “First and foremost, the thoughts of everyone connected to West Ham United are with Kurt and his family.
“To have someone break into your home is a terrifying experience and I hope this reward will help bring the individuals to justice and prevent others from going through a similar ordeal.”
Zouma missed the London derby with Crystal Palace due to “personal reasons” following the burglary. The 29-year-old has four children with his wife Sandra, who he first met when they were teenagers in Lyon.
The family have been described as “extremely distressed” by the ordeal.
A club statement read: “West Ham United has offered a £25,000 reward for information leading to the arrest and successful prosecution of burglars who broke into defender Kurt Zouma’s home on the eve of the Club’s Premier League fixture against Crystal Palace this weekend.”
A spokesperson for Essex Police said: “We were called shortly after 11.50pm on Saturday 2 December to reports of a burglary in west Essex.
“It was reported suspects had gained entry to an address, before taking items including jewellery and watches. Our investigation into this incident is continuing.”