The Occupy London demonstrators are camped on Leyton Marsh with local residents in a bid to prevent the building of the training hall.
Mr Justice Arnold issued an order “restraining unlawful activity” at the site yesterday.
About 20 demonstrators have been preventing trucks from entering the site after setting up camp.
Lawyers representing the Olympic Delivery Authority asked for an “urgent injunction” so that work could resume.
The BBC reported the ODA claimed campaigners had “harassed and threatened” construction workers building the centre on land known as Porter’s Field.
Planners gave permission on the basis that the centre would be demolished and land restored to its previous condition after the Games.
Mr Justice Arnold said the ODA was building the facility as part of an agreement with the regional park authority.
The injunction will run for 14 days, then the ODA will have to renew its application.
A Statement by the Save Leyton Marsh group said: “The ODA claim they have “no option” but to take legal action against this peaceful protest in order to fulfil their obligations “to provide practice facilities for the Olympic and Paralympic athletes”.
“This is fundamentally untrue. Eleven questions were put to them in December by a number of local councillors and still remain unanswered, including why the ODA chose not to utilize one of several alternative sites that would not require destroying this much loved green space.”