The Metropolitan Police said his condition is believed to be critical but stable, and his next of kin have been informed.
The driver, who did not require hospital treatment, has been arrested on suspicion of grievous bodily harm and taken to an east London police station.
A crime scene remains in place in the area.
Police have said there is nothing to suggest the incident is terrorism related.
One Twitter user wrote: “Major incident next to Leyton Midland road. Looks like someone has been seriously injured in the incident. About 20 police vehicles have arrived.”
Inspector Julia James from Met’s north east command unit, said: “This was a sudden and brutal attack on a uniformed officer carrying out their duties. What began as a routine vehicle stop has transformed very quickly and unexpectedly into an unprovoked attack with a weapon.
“Our thoughts are with the injured officer and his family and we wish him a full recovery. I would like to commend his bravery and resilience especially as he managed to draw a taser, despite being repeatedly stabbed, to prevent the suspect harming anyone else and to protect himself from further injury.
“My colleagues came to work that evening to protect and serve the community. Events such as this highlight the courageous work that police do every day, sometimes having to confront violent and dangerous individuals, who are determined to do them harm.
“This incident highlights the very real risk that police officers can be confronted with on a daily basis and the courage and professionalism officers demonstrate when doing their job.
“I would urge any witnesses to the incident to contact police via 101 quoting CAD3/8August or Crimestoppers anonymously via 0800 555 111.”
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