The women were in a car that crashed after being shot at near the settlement of Hamra, in the Jordan Valley.
The Magen David Adom ambulance service said two women in their 20s were declared dead at the scene. The third, who is 45, is in a critical condition.
The military said its troops had “started a pursuit of the terrorists”.
The incident was initially reported as a collision between an Israeli vehicle and a Palestinian vehicle, but when troops arrived they found several bullet holes in the Israeli vehicle, the military said.
The injured woman was taken by helicopter to hospital for treatment.
Israel Police commissioner Kobi Shabtai called on all Israelis with firearms licences to start carrying their weapons.
“This is a murderous attack that reminds us how relevant the threat of terrorist in its various forms is,” he said.
There has been an intensification of violence between Israel and the Palestinians since the start of this year.
More than 90 Palestinians – militants and civilians – have been killed by Israeli forces. If those behind Friday’s shooting are confirmed to be Palestinian, then 17 Israelis and a Ukrainian – all civilians, except for an Israeli paramilitary police officer – have been killed in Palestinian attacks.
Friday’s attack comes after the Israeli military said it had carried out air strikes overnight on targets linked to the Palestinian militant group Hamas in Lebanon and the Gaza Strip.
The military said the attacks were a response to a barrage of more than 30 rockets fired from Lebanon into northern Israel on Thursday, which it blamed on Hamas.
Militants in Gaza, which is governed by Hamas, fired 40 more rockets into Israel after the strikes began.
The barrage from Lebanon followed two nights of Israeli police raids at the al-Aqsa mosque in occupied East Jerusalem, which triggered violent confrontations with Palestinians inside and caused anger across the region.
