According to the Hebrew Wikipedia on the subject, There is no similar 48 hour delay before Prime Minister's resignation becomes official. That doesn't mean resignation is immediate. Quite the contrary.
There are two main differences between Prime Minister and a Minister, Knesset member and Knesset Speaker:
When Prime Minister has resigned or is voted out of office (the Knesset has the power to do so in a vote of no confidence) it means the whole government needs to be replaced (since the Prime Minister alone appoints all ministers).
There should never be any period of time when there is no Prime Minister in office. Also, there is no one that is automatically appointed as replacement for a resigned Prime Minister.
Therefore, in case of resignation or vote of no confidence, the Prime Minister (along with the whole government) remains in office until a new Prime Minister is appointed by the president and establishes his/her new government. In such a transitional government, there are no changes in offices.
The exception to the above rule is when the Prime Minister either dies or is rendered incapable of performing their duties. In this case, the vice PM takes the role of acting PM until a new one is elected or appointed. For example, after the assassination of PM Rabin, his vice, Shimon Peres, took office until the elections. After PM Sharon had a stroke, his vice, Olmert, took office until the elections.