The Levada Centre surveys political opinion among Russian people.
Its director, Lev Gudkov, said the move, which comes two weeks before parliamentary elections,  amounted to "political censorship".
Laws require all NGOs receiving any overseas funding to register as foreign agents and so face restrictions.
The Levada Centre cannot now conduct any work linked to the election campaign.
Mr Gudkov told Agence France-Presse news agency: "The consequences of such a decision for us are devastating - with such a label, we won't be able to work.
"This practically means the imposition of political censorship and the impossibility of independent polls. It's the typical behaviour of this repressive regime."
The other main pollsters are state-controlled.
The justice ministry said Levada had been "included in a register of non-commercial organisations that fulfil the functions of a foreign agent" following an unannounced document check.
Legislation passed in 2012 has designated as foreign agents a number of rights groups,  including Memorial, and the independent election monitoring group Golos.
The Moscow Times said the latest move followed a complaint by the pro-Kremlin Anti-Maidan movement over alleged US funding of Levada.
In May 2013, Levada had said it was being targeted for branding as a foreign agent and had suspended foreign funding.
The Russian authorities say the law is needed to protect Russia from outside attempts to influence internal politics.
But critics say it could be used to prevent NGOs denouncing vote-rigging and other abuses.
Russia's leading independent polling agency has been labelled a "foreign agent" by the justice ministry and says it cannot now work.