Around 700 people living at the building in Bow — about 2 miles (3.2km) from London's Olympic Stadium — have been contacted and warned that the weapons and about 10 troops are likely to be based at the site for around two months.
In a leaflet sent to residents, the ministry said the venue offered an uncluttered "view of the surrounding areas and the entire sky above the Olympic park."
Troops plan to conduct tests next week at the building, an upmarket gated apartment complex, to determine if the high velocity surface-to-air missiles will be stationed on a water tower attached to the site's roof.
Britain has previously confirmed that up to 13,500 troops are being deployed on land, at sea and in the air to help protect the Olympics alongside police and security guards. Defence Secretary Philip Hammond has said Typhoon fighter jets, helicopters, two warships and bomb disposal experts will also be on duty as part of the security operation.
"As announced before Christmas, ground-based air defence systems could be deployed as part of a multilayered air security plan for the Olympics, including fast jets and helicopters, which will protect the skies over London during the games," the defence ministry said in a statement.
"Based on military advice we have identified a number of sites and, alongside colleagues from the Metropolitan Police, are talking to local authorities and relevant landowners to help minimize the impact of any temporary deployments."
However, the ministry insisted that "no final decision on whether or not to deploy ground-based air defence systems for the games has been taken."
Resident Brian Whelan said those who live at the site were wary over the plan.
"From the few people I've spoken to, and the security we have here, they're not happy about it," he said. "I don't think it needs to be here at all."
The leaflet sent to residents insisted there would be no hazard to those living in the building.
It said the missile system would be "only authorized for active use following specific orders from the highest levels of government in response to a confirmed and extreme security threat."