Hamas downplayed the strike, saying the number participating was "very limited" but has threatened strip doctors of their private practices if they did not show up at public hospitals.
Basim Naeem, Hamas's health minister, said: "No one, no institution and no union will be allowed to sabotage the security of Gaza's citizens. We will not let anyone mock the health security of our citizens."
He threatened "the worst form of punishment" for those who do.
Hamas has also claimed the strikes are politically motivated and blamed the rival Fatah movement, which controls the Israeli-occupied West Bank.
Sami Abu Zuhru, a Hamas spokesman, said the strikes "follow calls issued by Fatah-run unions in Ramallah", in the West Bank.
"It is aimed at strengthening the blockade on Hamas, the Palestinian government, and the Palestinian people," he said, referring to the harsh restrictions imposed by Israel after Hamas took power in the Gaza Strip.
The health ministry also criticised the strike, saying that "these poisonous calls [to strike] come when there are more than 1,600 patients in desperate need of treatment and care".
But the Palestinian Authority's health ministry in Ramallah, said it was not involved in the strike but that it "understood the motivations for it, which come from the oppressive actions taken against our workers in the Gaza Strip".
The Palestinian Authority still pays the salaries of all civil servants in Gaza, including most doctors and health workers.
A similar strike in Gaza was held this time last year, when the Hamas-run government fired Jumaa al-Saqaa, a veteran surgeon and Fatah supporter, from his post as the spokesman for Gaza City's main Al-Shifa hospital.