Ms Cunningham, who is Scotland's longest serving elected parliamentarian, said it had been a "massive honour" to serve in both Westminster and the Scottish Parliament, and as part of the Scottish Government.
But with the next Holyrood election to take place in May 2021, the 69-year-old said her age had been a factor in her decision not to stand again.
Scottish Brexit Secretary Mike Russell has already announced he will not be seeking election in May, with other SNP MPs, such as Gail Ross and Bruce Crawford, also stepping down.
Ms Cunningham, MSP for Perthshire South & Kinross-shire, said: "It has been a massive honour to have represented my constituents in both Westminster and the Scottish Parliament for the past 25 years and to have been able to serve my country as a cabinet secretary in the Scottish Government."
Prior to becoming an MSP she was elected as MP for Perth and Kinross in 1995 - with Ms Cunningham going on to become the first SNP MP who won their seat in a by-election to hold it in the subsequent general election.
She thanked local activists in her constituency, saying: "They made history by making Perth & Kinross the first seat that the SNP would win at a by-election and hold at the subsequent general election, and they ensured that I became the longest-serving current Scottish parliamentarian."
But she added: "After a quarter of a century as an elected politician, and with another election fast approaching, I have had to do some hard thinking.
"By the time of the next election I will be less than two months away from my 70th birthday and, further, by the end of that parliamentary term I would be nearly 75. This year, of all years, has made age a rather more relevant factor than it may otherwise have been.
"I have, accordingly, taken the very difficult decision to inform my local constituency association that I will not be seeking nomination as an SNP candidate for the 2021 Scottish Parliament elections."
She was SNP depute leader between 2000 and 2004, and ran against Alex Salmond when he was elected party leader that year.
While born in Scotland, Ms Cunningham was brought up in part in Australia, after her family moved there.
And she said her "political journey began as a young girl in school in Western Australia", recalling that she left her teachers "bemused" when she wrote an essay calling for the then SNP leader Dr Robert McIntyre to come and speak at her school assembly.
Ms Cunningham commented: "Nobody then would have predicted that Scotland would be in the constitutional position it is today - or indeed that I would have played the part that I have been able to play."
She added: "Our country is in a very different place now than when I was first elected, the Scotland of 1995 was probably closer in many ways to the Scotland of 1965 than that of 2020."
Ms Cunningham previously served as community safety minister and the fair work, skills and training secretary before being appointed to her current role of Environment, Climate Change and Land Reform Secretary.
She stated: "There is much work still to be done to transform our country into the fair, green, just country I would like it to be.
"Some of that work will need independence for it to be accomplished, but there have been great advances that have benefited the country and my constituency. I am proud to have played my part."
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