The Barisan Nasional (National Front) coalition held onto the seat in a rural area of the eastern state of Pahang, considered a stronghold, with 61 percent of the vote, according to figures cited late Tuesday by state-run Bernama news agency.
The coalition had won the seat in 2013 with 67 percent of ballots.
Tuesday’s by-election was the first of two this week, with speculation rife over Najib’s future.
Najib’s reputation has been deeply tarnished in recent months by reports of his family’s extreme wealth, and revelations of alleged fraudulent overseas financial transactions by a debt-ridden, state-owned development fund, 1Malaysia Berhad (1MDB).
He launched the fund in 2009 and still serves as chair of its advisory board.
Najib has come under fire for declining to respond to demands from the opposition and from within his own party to explain the fund’s activities and the whereabouts of hundreds of millions of dollars in missing funds.
He also has faced a hail of criticism over the chaotic April 1 introduction of a new six percent consumption tax that has infuriated consumers, caused prices of some key goods to rise, and confused merchants.
Influential former Malaysian premier Mahathir Mohamad has led calls for Najib’s ouster over 1MDB, the Goods and Services Tax (GST), and accusations of weak leadership.
The GST emerged as a key issue in Tuesday’s by-election and in campaigning for the other vote set for Thursday in the northern state of Penang.
The Penang by-election is being held to replace opposition leader Anwar Ibrahim, who was jailed for five years in February on charges he sodomised a former male aide.
Anwar has called the case a “political conspiracy” by the ruling coalition to cripple the three-party opposition alliance that nearly took power in 2013 general elections.
His wife, Wan Azizah Wan Ismail, is among the candidates to replace him.
The Pahang by-election was necessitated by the April 4 death in a helicopter crash of the seat’s holder Jamaluddin Jarjis. (AFP)