The total number of confirmed in the PA-controlled areas was 41 by mid-Tuesday.
One of the new patients returned from Germany through the Allenby Bridge.
The second is a student from Ramallah who diagnosed also after he returned from abroad, PA government spokesman Ibrahim Milhem said.
He said that tests conducted on 30 people who came in contact with a Palestinian from Tulkarem, who returned from Poland and was diagnosed with the disease on Monday, showed they had not contracted the virus.
Another 14 Palestinians from Hebron who work in an Israeli factory have also tested negative for the coronavirus, Milhem added.
He said that a total of 2,885 samples have been tested for the virus since its outbreak in the West Bank.
Thirty-eight confirmed cases of the virus are in the Bethlehem area, which remains under lockdown for the second week.
PA Health Minister Mai Alkaila announced that all Palestinian travelers arriving through the Allenby Bridge would be required to remain in home isolation for 14 days as a precautionary measure to stem the virus.
In the Gaza Strip, where no cases of coronavirus have been registered so far, 95% of restaurants and hotels have been closed down, the Chamber of Commerce in the Hamas-ruled coastal enclave said.
It said the closure of the Erez border crossing has prevented 3,500 Gazans from working in Israel.
Fifty-one Palestinians have been placed in quarantine in a school in Rafah in the southern Gaza Strip upon their return from abroad.
Hamas, meanwhile, announced that it would release prisoners who spent two-thirds of their prison terms to prevent the spread of the virus in the Gaza Strip. The Hamas-controlled Interior Ministry did not say how many inmates would be released. It said that the inmates would be given “home leave” for one week, adding that the decision related only to those convicted of minor offenses.
On Tuesday, Hamas began work on building 1,000 quarantine rooms in the southern and northern Gaza Strip for Palestinians infected with the virus. Hamas leader Yahya Sinwar and senior Hamas officials were personally supervising the construction of the quarantine centers.