Police had detained a man thought to be planning a bomb attack on behalf of the extremist group, Turkey’s Anadolu news agency said.
The suspect was being taken to Istanbul’s main police station at around 11pm local time, escorted by two officers, when he stabbed one of them, police said.
The officer, named as Sinan Acar, was taken away by ambulance but died in hospital.
The attacker was shot dead but questions remain as to how he had managed to keep a knife with him after he was arrested.
Last year, Turkey suffered from a number of attacks that left hundreds of people dead. Some of these were blamed on IS jihadists and other on the outlawed Kurdistan Workers’ Party.
In July, dozens of alleged IS members were arrested and several were accused by police of preparing a “sensational attack” in Turkey.
Just minutes into New Year’s Day, a jihadist gunman attacked a night club in Istanbul, killing 39 people.