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.
Sir Malcolm has held a number of portfolios and was the first leader of the Scottish Liberal Democrats after the 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.
"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."
Scottish LibDem leader Willie Rennie said he had served with distinction, citing his role with the International Development Select Committee.