Sir Malcolm, 68, was elected as MP for Gordon, in Aberdeenshire, in 1983, having previously contested North Angus and Mearns and West Aberdeenshire. He has been elected seven times for Gordon.
He was made a Privy Councillor in 2005 and was knighted in last year's Jubilee Birthday Honours. He recently celebrated 30 years as an MP.
During his time in Parliament, Sir Malcolm has held a number of portfolios and he was the first leader of the Scottish Liberal Democrats after the new party was formed out of a merger of the Liberals and SDP.
He played a role in the Scottish Constitutional Convention which paved the way for the Scottish Parliament.
Sir Malcolm said: "It will be strange not being a candidate for the first time in over 40 years but I believe it is right to stand down when I am still enjoying what I do and have energy for other things. I have spent 10 years away from home in my time as an MP and, having a young family, I hope I can give them more time and attention.
"I joined the Liberal party as a student because I did not believe that other parties championed liberal values which represent the greatest political philosophy Britain, and especially Scotland, have given to the world.
"I am pleased to have played a part in delivering a Scottish Parliament. When I joined the party we had six MPs and a small national vote. It pleases me to have been part of a process that has seen the party grow to a truly national movement and a party of government delivering policies I helped develop.
"This Parliament has been tough. Being in Government doesn't always make you popular. But we are a serious party. We have accepted responsibility to try and turn the economy round. We have cut taxes and boosted pensions. We have delivered more powers to Scotland.
"I believe people can see the difficult decisions we have taken are beginning to have a positive effect and I am confident that the party can do well at the next election. I look forward to working with my successor as Liberal Democrat candidate and ensuring that we return a hard-working Liberal Democrat MP for the benefit of the people of Gordon."
The Scottish party's leader, Willie Rennie, said: "Sir Malcolm has represented his constituents in Gordon and the Scottish Liberal Democrats with distinction over the past 30 years. He has made a substantial contribution to Scottish and British politics over this period, not least as chair of the International Development Select Committee.
"As a young Liberal Democrat I had the pleasure of working with Malcolm while he was leader of our party in Scotland. Despite being hugely busy, he always found time to sit and talk, offer advice and tell us about his own experiences in the House of Commons. This was a pattern repeated after I became an MP when he took the time to answer my questions.
"Malcolm has been a stalwart of our party over the past 30 years. He has worked tirelessly for his constituents since first elected I am certain he will continue to do so until his last day in office."