The killing casts another shadow on US-mediated Israeli-Palestinian peace talks that resumed in July.
The deaths of several Palestinians in Israeli raids to detain militants has also caused tensions, with Palestinians cancelling one session in response.
The 20-year-old soldier was reported missing late on Friday and Israeli forces began searching for him, before arresting Nidal Amar, 42, a Palestinian from Beit Amin in the northern West Bank.
Amar confessed to killing the soldier, identified as Sgt Tomer Hazan, whom he knew through working together in a restaurant in Bat Yam in central Israel.
According to Shin Bet intelligence agency, Amar admitted picking up Sgt Hazan in a taxi on Friday after convincing him to accept a ride. He then took him to an open field, killed him and hid his body in a well, the agency said. Israeli forces raided Amar's home yesterday, arresting him and a brother. Amar is said to have confessed to intending to trade Sgt Hazan's body for another brother.
The latest death only increases mistrust between the two sides, whose negotiations resumed following US Secretary of State John Kerry persuading them to get back behind the table after talks collapsed in 2008.