According to Sky News, the court said the possible length of US jail terms - life without parole - raised concerns about breaches of the European human rights code and needed further examination before a final ruling.
Ahmad, a 36-year old computer expert, has been in a UK prison without trial for nearly six years, refused bail since his arrest in August 2004 on a US extradition warrant.
Radical preacher Hamza is also wanted on terror charges in the US.
Both appealed separately to the European Court of Human Rights on the grounds that their treatment and potential punishment could violate Human Rights Convention provisions on the "prohibition of torture and inhuman or degrading treatment".
A statement from Ahmad's family said: "We are very pleased with today's ruling by the European Court of Human Rights that Babar's extradition should be temporarily frozen due to deep concerns it has regarding possible "cruel and unusual punishment" of Babar if sent to the United States. (ANI)