A government statement said the decision had been taken to protect Ukraine's "national security".
Hours earlier MPs rejected a bill that would have allowed jailed opposition leader Yulia Tymoshenko to leave the country - which the EU had demanded as a condition for the deal to proceed.
Ukraine had come under intense pressure from Russia not to sign the historic EU deal at a summit next week.
The Ukrainian government said on Thursday that it was instead looking into setting up a joint commission to promote ties between Ukraine, Russia and the European Union.
Russian officials said they welcomed any Ukrainian moves to foster closer relations.
Russia wants Ukraine to join its own customs union with Kazakhstan and Belarus, which it sees as a prototype rival to the European Union.
The EU's foreign policy chief Catherine Ashton called the decision a "disappointment".
"We believe that the future for Ukraine lies in a strong relationship with the EU," she said in a statement.
Ukraine's President Viktor Yanukovych was later quoted by AFP as saying Ukraine "will work further on this path... to EU integration" - although it is not clear how this will now be achieved.
Stefan Fuele, European commissioner for enlargement, cancelled a trip to Kiev after news of the decision broke.
He had been due to travel to the Ukrainian capital for the second time this week on Thursday.
He tweeted that it was "hard to overlook in reasoning for today's decision [the] impact of Russia's recent unjustified economic & trade measures".
Swedish Foreign Minister Carl Bildt went further, saying Ukraine had "bowed deeply" to the Kremlin, which he accused of using the "politics of brutal pressure".
Shouts of 'shame'
On Thursday MPs threw out six drafts of the bill which would have allowed Tymoshenko to travel abroad for medical treatment.
The bill that would have allowed Tymoshenko to leave the country failed to pass after MPs from Mr Yanukovych's ruling Regions Party refused to cast their votes on any of the six proposed drafts.
The drafts all fell short of the 226 votes needed.
"It is President Viktor Yanukovych who is personally blocking Ukraine's movement toward the European Union," Arseniy Yatsenyuk, parliamentary leader of Tymoshenko's opposition Fatherland group, told parliament after the vote failed.
Tymoshenko, 52, is serving seven years in jail after a controversial conviction on charges of abuse of power over a gas deal with Russia.
The EU has made clear it believes the judicial campaign against Tymoshenko has been politically motivated.
She has been urging the authorities to transfer her to a German hospital so that doctors there can treat her chronic back pain.
The EU is demanding her release as one of the conditions for signing an EU-Ukraine trade and partnership agreement.
It has been attempting to build closer relations with neighbours that were once part of the Soviet Union, and is expected to initial but not yet formally sign association agreements with Georgia and Moldova.