The pedestrian was involved in a collision with a car at about 2.15pm yesterday on Victoria Road West.
The man - who has not been named - was taken to hospital with serious injuries, where police say he remains in a critical condition.
Officers are now appealing for those who may have witnessed the incident to come forward with any information.
A spokesman for Northumbria Police said: "We are appealing for information after a serious collision between a car and an elderly pedestrian in Hebburn.
"At about 2.15pm, a red Ford Fiesta was travelling on Victoria Road West when it collided with an 87-year-old pedestrian near to the junction of South Drive.
"Emergency services responded and the pedestrian was taken to hospital with serious injuries. He remains in a critical condition.
"The driver was spoken to by officers at the scene.
"They were not injured but left very shaken by the incident."
The road was closed for a number of hours, but reopened last night.
The police spokesman added: "A road closure was put in place after the incident to allow officers to carry out their investigation but that has since been re-opened.
"Inquiries into the incident are ongoing and police are now appealing for any witnesses to come forward.
"Officers particularly want to speak to any motorists who were driving in the area at the time and may have dash board footage that can be reviewed by police.
"If you can help police then please get in touch by calling 101 quoting ref 613 16/11/17."