The United States, Israel's closest ally, had urged a crackdown on settler violence and the arrest of the perpetrators of the attack on the photojournalist.
France, Belgium and Poland, whose diplomats were attacked, also called on Israel to take action.
The suspects were arrested in a pre-dawn operation on suspicion of involvement in acts of violence, violating a closed military zone order and illegal construction, police said on Monday.
The suspects, whom police did not identify, were taken into custody for questioning. Israel's Army Radio reported that they were Israeli citizens.
Prosecutions of Israeli settlers are rare.
A video released by the police of the pre-dawn operation appeared to show at least one arrested suspect, whose face is not seen, wearing ritual tassels known as tzitzit, which are often worn by observant Jewish men.
The video also appeared to show two slingshots, which can be used to hurl stones, being found at one property.
On Friday, when the Washington Post journalist was attacked, dozens of masked settlers, some armed, descended on a Palestinian olive harvest, with some settlers hurling stones with slingshots.
Police, military forces and the Shin Bet domestic security service took part in the operation.
Referring to the West Bank by its biblical name, Judea and Samaria, Israeli police commissioner Daniel Levy said the law applied to everyone, "regardless of identity or affiliation".
"The Israel Police is committed to professional, equal, and impartial law enforcement, based on evidence and in accordance with the law," he said in a statement announcing the arrests.
Masked Israeli settlers were filmed on Friday assaulting Washington Post photojournalist Heidi Levine, a US citizen, who was covering a Palestinian olive harvest in the West Bank. Levine was taken to hospital and underwent surgery on a finger.
On Saturday, French, Belgian and Polish diplomats as well as a French mayor were attacked by masked settlers in another part of the West Bank. A Belgian diplomatic vehicle was also damaged.
Israeli Foreign Minister Gideon Saar and the military have blamed "Israeli rioters" for the attack on the diplomats.
However, Prime Minister Benjamin Netanyahu, whose religious-nationalist coalition is projected to lose its governing majority at the October 27 election, has been more circumspect.
He has said the diplomats entered a "sensitive area with a history of confrontations" and without co-ordinating with the military. He has also said that the facts of the attack on Levine were "unclear".
From her hospital bed on Sunday, Levine said she was "shocked and insulted" that Netanyahu had cast doubt on the attack.
US Ambassador Mike Huckabee condemned the attack as a "despicable act of terror carried out by masked cowards" and said they should spend years in prison. Israel's president and several opposition politicians also spoke out against the attack.
Levine has said she was attacked by masked men wearing tzitzit tassels.
Israel's President Isaac Herzog has apologised, saying the "violent rioters" who "brutally attacked" her did not represent the values of Israel.
Settler attacks on the Palestinians are surging, with at least 170 since September 27, according to Yesh Din, an Israeli human rights group.
Journalists, Israeli activists and foreign observers have also been targeted.
United Nations bodies and most countries deem the settlements illegal under international law but Israel rejects this, viewing the territory as disputed rather than occupied.
with AP
