The NJ Transit driver was about 1,000 feet from reaching the New York side when he had the seizure just after noon on Wednesday.
He lost control of the bus, which struck four cars before coming to a stop.
The driver and at least two occupants of other vehicles were taken to the hospital for non-life threatening injuries.
Both lanes of traffic in the south tube, where the accident occurred, were closed for the investigation.
Manhattan-bound traffic used one lane of the center tube, but delays were still significant.