The decision was taken in a meeting of the Board of Approval (BoA), headed by Commerce Secretary Rita Teaotia, on August 12.
"After deliberations, the board rejected the proposal due to lack of recommendation from the state government," the minutes of the BoA meeting said.
Infosys had proposed to set up IT-ITeS SEZ over an area of 20.14 hectares in South 24 Parganas.
The state government's recommendation is important to get approvals from the BoA.
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The developers who got the formal approval includes Devbhumi Realtors, Phoenix Living Spaces and Phoenix Embassy Tech Zone. All these three plans to set up IT/ITeS zones in Telangana.
While Chhindwara Plus Developers got approval to set up a multi-product SEZ in Madhya Pradesh, it wants to set the zone over an area of 1,320.06 hectares.
SEZs are exports hubs, which contribute about 16 per cent to the country's total outbound shipments.
The commerce ministry is taking steps to revive investors interest in these zones. It has asked the Finance Ministry to extend sops like rollback or reduction in the minimum alternate tax.
Exports from special economic zones (SEZs) logged a marginal growth of 0.77 per cent to Rs 4.67 lakh crore in 2015-16.
The exports from such 204 zones were Rs 4.63 lakh crore in 2014-15.
Highest number of SEZs are operational in states like Tamil Nadu, Karnataka, Telengana and Maharashtra.