Ramnik Narsey, the new chief, had joined the retail giant in May 2013.
The appointment will be effective January 20, 2014, the company said in a statement.
Former Walmart India head Raj Jain has been roped in as an advisor by the Bharti Group, which on Wednesday parted ways with the US retail giant to operate stores independently in India.
Scott Price is learnt to have conveyed to Sharma that Walmart remained committed to the India market.
Sources estimated the number of employees asked to leave because of downsizing stands at about 100.
This could mean an end to the talks for a possible partnership between the two firms in the multi-brand retail space -- less than a year after 51 per cent foreign investment was allowed in the sector.