He said his office was told Mr Sabin - who was also the chairman of the law and order select committee - intended to resign only on Thursday.
The by-election to replace the Northland MP is expected to cost taxpayers close to $1 million.
Mr Sabin said on Friday that he had resigned "due to personal issues that were best dealt with outside Parliament".
A spokeswoman for the Electoral Commission said the cost of holding a by-election varied from electorate to electorate, but past byelections had cost around $900,000.
Mr Key said a byelection in the Northland electorate was likely to be held in mid-to-late March but it is up to the Speaker's Office to formally note the vacancy and announce the date.
National is likely to want to hurry the byelection along because Mr Sabin's departure leaves the party with just 59 seats in a 121-seat Parliament and makes it even more dependent on support parties to get legislation through the house.
Mr Sabin was a former police detective in Northland and formed the company MethCon after leaving the Police as part of his efforts to increase awareness of the dangers of methamphetamine.
He sold the company the year before he entered Parliament. In 2009, his son Darryl suffered a brain injury while playing rugby and Mr Sabin spoke out publicly about Darryl's struggles in recovery.
Mr Sabin's main rival in last year's election, Labour candidate Willow-Jean Prime, is keen to contest the seat again - despite having her first child just last week.
Ms Prime, a lawyer and Far North District councillor who lives near Moerewa, said she had already contacted the party's general secretary, Tim Barnett, to say she wanted to stand in the byelection.
In the 2014 general election she won 8969 electorate votes to Mr Sabin's 18,269, reducing his majority by more than 2000 votes from the 2011 election.
Mr Key said today he was confident National would be able to hold onto the seat.
"We've held that seat for a very long period of time," he said.
"If you look in the Far North, John Carter's held the seat for a long time prior to Mike Sabin. Mike Sabin was a good, hard-working local MP."