Police said the 25-year-old Jewish victim was in a serious condition after being stabbed in the neck near one of Jerusalem's main thoroughfares.
The incident occurred near a tramway station close to the national police headquarters, police said.
The suspect, said to be from Shuafat refugee camp in annexed east Jerusalem, later attacked a tramway guard and tried to take his gun before fleeing. Police initially gave his age as 15 before later correcting it to 19.
"He was arrested by police special forces who were in the area," police spokesperson Luba Samri said.
There has been a series of knife attacks by Palestinians on Israelis in recent days as rioting has spread across east Jerusalem and the occupied West Bank.
At least four knife attacks have occurred in Jerusalem and six overall since Saturday, when a Palestinian killed two Israelis in the Old City, helping prompt an Israeli security crackdown.
Rioting in east Jerusalem and the West Bank has seen youths throwing stones and firebombs face off against security forces firing rubber bullets, tear gas and stun grenades.
Over the past week, four Israelis have been killed and five Palestinians, three of them after alleged attacks on Israelis.
The unrest has sparked fears of a broader uprising, even a third intifada.
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