The British driver has made a disappointing start to his first season with Ferrari as he is yet to finish on the podium in 14 races and the sport's former ringmaster believes that the seven-time world champion should bring his glittering career to an end.
Ecclestone, 94, told the Daily Mail newspaper: "Lewis is very talented, was and probably still is. But like a lot of leading sports personalities when they reach the top, there is only one way to go and it’s not a good direction. It’s only down.
"They get tired. Lewis is tired. He’s been doing what he is doing forever. He needs a rest from it for good, a total reset to do something completely different. He may not think it, but he will soon get used to doing other stuff away from motor racing.
"I think he should have done it a while ago."
Ecclestone has urged Hamilton, 40, to get his big-money Ferrari contract paid out in full and believes that the racer would be "cheating himself" if he continues with his career any longer.
He said: "The guy is not a cheat, but he would be cheating himself if he goes on.
"He should stop now. If I were looking after him I would negotiate with Ferrari immediately and say, ‘If you have someone to replace Lewis, he’ll step aside.’
"If I were Lewis, I would say to Ferrari that I wanted to be paid all my contract, in full. They signed him because they thought he could do a job. ‘It isn’t working so I can make way if you want me to’… but that’s the arrangement."
Hamilton had branded himself "useless" after only finishing in 12th place at the Hungarian Grand Prix at the weekend but insisted that he will be back when the sport returns from its summer break in the Netherlands later this month.
The 105-time race winner said: "I look forward to coming back, hopefully I will be back, yeah."