Medics evacuated her to Jerusalem’s Shaare Zedek Medical Center, the Magen David Adom rescue service said.
The attacker approached the woman – later identified as hailing from Nepal – from behind as she waited at a bus stop on Shamgar Street, stabbed her in her upper back and fled.
The woman was taken onto bus number 418 that stood open at the stop, where medics treated her wound.
Medics said she is fully conscious and stable.
The terrorist fled the scene, triggering a manhunt after him in nearby buildings and streets, according to police.
Shortly after 11 a.m., police said they located the man hiding in a construction site nearby. He was identified only as a West Bank resident, and police said he matched descriptions provided by eyewitnesses to the attack.
The suspect was handed over to the special investigations unit of the Jerusalem Police for questioning.