In an official response to the city council, the Lothian and Borders force said the developers need to pay more thought to the risk of a terrorist attack.
The officers' main concerns relate to plans for an underground car park, which they said requires the "highest possible standards" of control to prevent an explosion being set off under the main stand. A hotel at the stadium, which is part of majority shareholder Vladimir Romanov's vision for the site, also lacks "any protection" from terrorist groups, the police said.
Other problems highlighted include the lack of space behind the stadium for emergency vehicles – an area which also acts as an escape route – and arrangements for delivery vehicles, which could allow uncontrolled access to the ground.
Hearts submitted a formal planning application to the local authority earlier this year, and councillors will consider the proposals in the coming months.
In his letter to the council, Pc Andrew Cameron – divisional architectural liaison officer with A Division – said: "In the current climate, sports stadia and areas of mass gatherings are regarded as potential targets by terrorist groups operating in this country.
"The most likely means of delivering such an attack is by vehicle-borne improvised explosive device (VBIED), as seen last year in London and at Glasgow Airport.
"The lack of any protection or defensible space for the hotel building, including the pillars, causes some concern. In addition, there is a possibility of parking a VBIED within the underground car park before a game."
Pc Cameron also suggested the car park should be built to absorb such a blast, which would protect supporters in the stand above.
The Gorgie club wants to demolish its dilapidated main stand and construct a state-of-the-art replacement, bringing stadium capacity to around 23,000 by 2010.
The new two-tier, 10,000-seat structure will incorporate administration offices, commercial office space, residential apartments and conference and banqueting facilities. There will also be leisure facilities such as a bars, restaurants, and a gym on site.
The multi-million pound project will mostly be funded by Ukio Bankas Investment Group, Hearts' parent company, which is owned by Mr Romanov.
A spokesman for Hearts said consultation with the police is ongoing. "We are aware of the comments that have been made by the police, and they don't pose any due concern for the club in terms of the planning application.
"We studied the issue of security and safety as a priority, prior to submitting the application. We are confident that the measures in place will be first class."
BATS COME HOME TO ROOST AT NEW GROUND
HERITAGE watchdogs have called for bats to be provided with better roosting facilities at Hearts' redeveloped stadium.
In a letter sent to the city council, Scottish Natural Heritage said bats are known to currently roost in the western Wheatfield stand, and possibly underneath the northern Roseburn stand.
Although these areas will not be affected by the 51 million redevelopment of the main stand at Tynecastle, the body has recommended the installation of bat boxes.
Edinburgh area officer Carolyn Clark said: "Scottish Natural Heritage has no objection to this proposal. However, we would recommend a condition is in place to protect and enhance the bat roost provision.
"A bat box is also recommended at the west stand to provide a better alternative roost to the existing one.
"The council should ensure that these recommendations are incorporated into the development by way of planning conditions."