Mr Suga had been appointed to the role just a year ago following the resignation of Shinzo Abe.
The shock announcement comes as Mr Suga’s approval ratings dropped to an all-time low.
Japan – which is still under a state of emergency – is now grappling with its worst ever Covid wave.
The country, which has now seen more than 1.5 million virus cases, has also seen a slow vaccination roll out.
The decision to host the Olympics Games this year despite the worsening pandemic also proved to be hugely unpopular.
“Today at the executive meeting, [Mr] Suga said he wants to focus his efforts on anti-coronavirus measures and will not run in the leadership election,” said the secretary general of Mr Suga’s Liberal Democratic Party (LDP), according to an AFP report.
“Honestly, I’m surprised. It’s truly regrettable. He did his best but after careful consideration, he made this decision,” he said.
Japanese shares rose sharply on the news, with the broad Topix stock index closing up by 1.6% after hitting its highest level in three decades.
Tokyo’s financial markets had made gains already this week on hopes for a stronger government ahead of the ruling party’s leadership race and a general election later in the year.
The 72-year-old, who was born to a family of strawberry farmers, was first elected to the Yokohama City Council in 1987, and in 1996 he was elected to Japan’s Diet for the first time.
In 2005, Prime Minister Junichiro Koizumi appointed him senior vice minister of internal affairs and communication.
The following year, Mr Koizumi’s successor Shinzo Abe promoted him to minister with three cabinet posts, which he held until 2007. Source: BBC