Leake, 32, was scheduled to make $16 million for a full season in 2020 and was positioned to be fighting for a spot at the back end of the rotation. He will be a free agent next season.
"This was not an easy decision for Mike," Leake's agent, Danny Horwits, said in the statement. "He wishes the best of luck and health for his Diamondback teammates this season and he's looking forward to 2021."
The specific reasons for Leake's opt-out were not clear. Horwits said Leake and his family had many discussions about playing, taking "countless" factors into consideration. Horwits said many of the considerations were personal to Leake and his family.
Diamondbacks general manager Mike Hazen also said two players on Arizona's 60-man roster tested positive for COVID-19, as did another player not in Arizona.
Leake was listed on the Diamondbacks' 60-player pool released earlier Monday but will be moved in a later transaction.
"It definitely impacts us,'' Hazen said. "Certainly, he's a good major league starting pitcher. To what extent it's going to impact us, it's hard to say. I think I would probably have a different answer if it was over 162 [games] as opposed to if it was over 60.''
The Diamondbacks also will be without two international prospects due to travel issues during the pandemic: outfielder Kristian Robinson of the Bahamas and Brazilian right-hander Bo Takahashi.
Right-hander Silvino Bracho was not on Arizona's 60-man roster to start the season after he suffered elbow stiffness while trying to rehabilitate from Tommy John surgery last year.
Leake, a 10-year veteran who had stints with the Reds, Giants, Cardinals and Mariners, was acquired by the D-backs at the trade deadline from Seattle. He started 22 games for the Mariners in 2019, with a 9-8 record, two complete games and a 4.27 ERA. He was 3-3 with a 4.35 ERA in 10 games for Arizona.
He led all major league pitchers in home runs allowed last season with 41. He has a lifetime record of 105-98 and an ERA of 4.05.
The Associated Press contributed to this report.