A club statement said: "His passing will come as an enormous shock to everyone but most particularly, of course, to his family and friends.
"Our thoughts are with them at this time. To say he will be missed is an unmistakeable understatement."
The statement added: "Anyone who came to know Markus learned of his quick wit, love of football - most especially Saints football - and his unquenchable thirst for better knowledge of all things.
"Anyone who had the privilege of meeting Markus met a man who was quiet, unassuming, undemonstrative and fantastic fun to be with.
Not only did he save our fantastic football club, he rebuilt it, forming strong foundations at every single part of the club
JonnySFC
"The welcome that Markus was given when he arrived at the Saints just over a year ago was something that gave him a deep sense of pride and satisfaction. The progress of the Saints was always uppermost in his mind.
"He would have wanted to be there when the Saints get promotion to the Premier League.
"The well-laid plans for the club that he and the executive chairman [Nicola Cortese] had mapped out over a year ago will continue to be implemented uninterrupted and nothing will change in that regard.
"The club will ensure that Markus' wishes are carried out in full. The Saints were Markus' constant preoccupation. He certainly didn't like losing.
"And his constant ambition was to see open, attacking football played to the highest possible standard. To Markus, last year was the start of getting the Saints back on the march."
Southampton won the Johnstone's Paint Trophy and finished seventh in League One, missing out on a play-off place by seven points after starting the season with a 10-point penalty, in Liebherr's only season as owner.
The club said a memorial service would be held in due course and that a book of condolence would be available for fans to sign.
Source: BBC Sport
Source: BBC Sport