Gold, who together with fellow businessman David Sullivan took a controlling share of the club three years ago, fell ill following the Hammers' FA Cup third round clash with Manchester United on Saturday.
The 76-year-old took to Twitter on Friday to thank well-wishers, saying: "Good morning. I'm over the worst. Still on intravenous antibiotics but feeling better. Thank you so much for your kind words of support. Dg".
News of Gold's illness first broke when daughter Jaqueline tweeted: "Have taken my father into hospital.
"I think he's learnt a very harsh lesson not to go to football with bronchitis. Now has pneumonia and being assessed."
She added that her father was on 'very strong antibiotics.'
In March 2011, 76-year-old Gold needed hospital treatment for cholangitis and septicemia.