The New Zealand international, who sprained an ankle in training earlier this month, was operated on at a London hospital.
The operation was a success but, according to a statement on the West Ham website, "no timescale has yet been set for a return to first-team action".
The club's head of sports science and sports medicine Andy Rolls said: "Winston had an operation on his ankle injury to stabilise the joint. This procedure went well.
"He will now convalesce for a few days before starting his rehabilitation."
Reid's fellow defenders James Collins and Joey O'Brien withdrew from international duty this month, but Sam Allardyce is hopeful both will be fit to face Chelsea on Saturday.
Razvan Rat is a doubt after suffering a hamstring injury while away with Romania.
Watch West Ham take on Chelsea live on Sky Sports 1 at 5.30pm this Saturday