The governor general, Sir Frank Kabui, announced the date yesterday and also informed MPs that nominations for the top job opened today and would close on Thursday.
Each prime ministerial candidate must be nominated by four MPs.
MPs cast secret ballots in the vote which will start at 9:30am at parliament.
In order to win, a candidate must secure an absolute majority of the 50 votes.
If there are several candidates and an absolute majority cannot be achieved voting will continue by rounds of elimination.
Two main coalition groups of MPs have formed since the general election two weeks ago.
One group contains the former prime minister Rick Hou and the other has members of the last opposition as well as prominent newly elected MPs, including Peter Kenilorea Jr.
Mr Kenilorea is the son of Solomon Islands' first prime minister.