Israeli troops raided the Aqbat Jabr refugee camp near the city at dawn and was met with armed Palestinians, leading to exchanges of fire.
Palestinian medics said three more Palestinians were wounded, one of them in critical condition. No Israelis were hurt.
The incursion followed nearly two weeks of Israeli closures and checkpoints on Jericho’s entrances and exits.
The Israeli army ramped up operations and raids in the city after a report of a shooting at a restaurant frequented by settlers in the city on 28 January. No casualties were reported at the time.
The army said two Palestinians suspected of being behind the restaurant shooting were among those killed on Monday.
On Saturday, an Israeli raid on Aqbat Jabr camp was met with heavy gunfire by Palestinian fighters who appeared to be members of Hamas' armed wing, the Qassam Brigades.
Jericho, located northeast of Jerusalem, is a West Bank city that rarely witnesses violence.
Hamas leader Ismail Haniyeh mourned those killed in the raid as “heroes”.
“Despite the heinous massacre, the [Qassam] Brigades will continue its operations along with all revolutionaries of our people until we defeat the occupation,” he said.
On Friday, Israeli forces shot Abdullah Sami Qalalweh, a 26-year-old unarmed Palestinian, near the town of Huwara, south of Nablus.
A total of 41 Palestinians have been killed by Israeli fire this year, 35 of whom were killed in January - the deadliest month in the West Bank since 2015.
Violence has spiked in recent days following an Israeli military raid on the Jenin refugee camp on 26 January in which 10 Palestinians were killed.
A day after the Jenin raid, a Palestinian gunman killed seven Israeli settlers in a shooting in an occupied East Jerusalem settlement.
According to data compiled by Middle East Eye, Israeli forces killed more Palestinians in the occupied West Bank in 2022 than in any single calendar year since the Second Intifada. Palestinians killed 30 Israelis in various attacks in the same period.