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.
The Northern Advocate understands the party's Northland branch officials have been canvassing for a potential candidate for several weeks.
Prime Minister John Key refused to comment on when he first found out Mr Sabin's personal issues, but said National had not asked Mr Sabin to step down. 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.
"Mr Sabin reached that conclusion himself on the back of personal and family reasons he is pursuing. He's obviously made the best decision for himself and his family."
He said Mr Sabin had been a good local MP and cited his anti-drug work as valuable for National.
Mr Key said he was confident National would win the byelection in Northland and believed Mr Sabin was highly regarded in the electorate.
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.
Labour would now start its selection process or, if no other nominations were received, confirm Ms Prime as its candidate.
Ms Prime and her husband Dion Prime, a teacher at Bay of Islands College, had their first child last Saturday.
Hihana Prime was born at Whangarei Hospital weighing 3740g (8lb 4oz). The name is a transliteration of Ms Prime's sister's name, Season.