The injury forced the Indian ace to pull out of the Sony Ericsson Open last month.
"A recent MRI showed contusion of her lunate bone with some inflammation and a suspected tear in the volar capsule. She is undergoing arthroscopy to repair the capsule and to clean out debris formed from chronic inflammation," a statement from Globosport said.
'Sania should put in that extra effort'
"Reknowned hand specialist Dr Badia will perform the surgery," it added.
Sania arrived in the United States on Tuesday accompanied by her mother and physiotherapist Renuka Pinto.
She earlier underwent knee surgery in March 2007.
Photograph: Greg Wood/AFP/Getty Images