Is Hyderabad considered as a Metro city in HRA calculation

no

as per the income tax act it is not considered as metro city.

No it is not considard a metro city

Only four cities are considered as metro in regarding to HRA

They  are

Delhi, Mumbai, Chennai, kolkotta

According to Government of India, Ministry of finance, GHMC upgraded as A-1 Class (Metro) city for the purpose of HRA (only Central Govt. Employees).

Memorandum released on 31st August, 2007. orders effected from 1st September, 2007.