Corporation commissioner Amarjeet Singh told reporters that the structures were a major part of the academy. It included two buildings and a toilet block.
"The construction is completely banned in green belts of Shimla," Singh said.
The official also said that if the HPCA fails to demolish the structures, the corporation would demolish it.
Officials said the corporation had sent three notices to the HPCA from August 2012 to October last year and the cricket body has failed to reply.
The cricket academy is in the thick of controversy as the mayor and the deputy mayor had alleged that the land was leased out to the HPCA without prior permission of the corporation house.
The cricket academy is part of the HPCA properties that were taken over by the government in a mid-night swoop October 26 last year and then handed back to the cricket body on the direction of the High Court.
District Cricket Association president Surinder Thakur said the HPCA would challenge the order of Shimla corporation in a court.
The state vigilance bureau has already filed a cheating and misappropriation case against the HPCA over alleged wrongdoings in allotment of land, which according to revenue records was the common village land, to the sports association for constructing a residential complex for the players near the stadium in Dharamsala.
The disputed land, three kilometres from the picturesque international stadium, has been used by the HPCA to build a five-star residential complex called The Pavilion, which has 38 rooms, 32 huts and a high-tech gym.
The land was allotted when a Bharatiya Janata Party government, headed by Prem Kumar Dhumal, was in power in the state.
HPCA president Anurag Thakur, who was questioned by the vigilance bureau in November last, is the son of Dhumal.
The HPCA has also been accused of encroaching upon land of the state sports and youth services department.
--IANS (Posted on 08-01-2014)