Up to 30 men, some with false beards and one masquerading as a pregnant woman in a wheelchair, entered the hospital in Hebron overnight.
They took away a suspect in a recent stabbing near Hebron after shooting dead his cousin in an altercation.
Ten Israelis and dozens of Palestinians have been killed in recent unrest.
Many of the Palestinian fatalities were attackers in near-daily stabbings of Israelis, shot by their victims or security forces.
The surge in violence began in September when tensions at a flashpoint holy site in Jerusalem revered by Jews and Muslims boiled over, amid rumours that Israel planned to relax long-standing rules to strengthen Jewish rights at the complex.
Israel has repeatedly denied such claims.
Closed-circuit television footage from al-Ahli hospital showed a large, armed group disguised as Arab men and women making their way down a corridor, pushing the wheelchair, shortly before 04:00 (02:00 GMT).
They point the guns at hospital staff, apparently ordering them to stay back.
Minutes later they are seen making their way back with the suspect, 20-year-old Azzam Shalaldeh, in the wheelchair.
Mr Shalaldeh is alleged to have stabbed and wounded an Israeli on 25 October before escaping after being shot by the victim.
Palestinian officials said Mr Shalaldeh's 27-year-old cousin, Abdallah Azzam Shalaldeh, was shot and killed in Azzam Shalaldeh's hospital room.
Israel's Shin Bet security agency said he was shot after attacking the Israeli forces. Azzam Shalaldeh's brother Bilal, who was also in the room at the time, said Abdallah Azzam Shalaldeh was shot without warning when he emerged from a bathroom.
Shin Bet said Azzam Shalaldeh belonged to "a family of Hamas militants", AFP news agency reported.
The Israeli military operates an undercover unit colloquially known as Duvdevan, which sometimes mingle undetected with Palestinians during riots before snatching suspects.
An undercover team also carried out a raid on a hospital in the West Bank city of Nablus last month, seizing a suspect in the murder of an Israeli couple days earlier.
Undercover Israeli forces shot dead a Palestinian and seized a stabbing suspect in a raid on a West Bank hospital, Palestinian officials say.