Ecclestone has been head of the Formula One show for more than 40 years, but his leadership is currently under scrutiny as he is facing two separate court cases.
He has been indicted in Germany for bribery in a case related to the sale of a F1 stake to banker Gerhard Gribkowsky of Bayern Landesbank (Bayern LB) eight years ago.
Meanwhile in London, German media group Constantin Medien is claiming damages of US$171million (Â£111million) as they feel the 47.2 per cent stake in the sport previously owned by bank Bayern LB was sold too cheaply in 2006 to CVC Capital Partners, the current commercial rights holders of the sport.
Despite the pressure from all corners, Horner says the sport would be "unimaginable" without Ecclestone.
"Bernie is a unique individual who has run Formula One tremendously successfully for the last 40 or 45 years," he said.
"The business, as it is today, is because of the way he has run it and operated it. It is unimaginable for him not to be there."
Horner added: "It's obviously very difficult for us to judge the issues (Ecclestone) is currently dealing with, but I'm sure he is fully focused.
"So long as Bernie is able to run the business, then he is absolutely the right guy to be running it. It's as simple as that.
"And he has the full backing of the shareholders of Formula One."
Some have suggested that Horner could replace Ecclestone when he eventually decides to call it a day, but when asked if he had sounded out by the man himself, he replied: "No, not at all. I'm fully focused on what I'm doing.
"Bernie is a remarkable guy, and I doubt he has given much thought to succession to be honest with you because he is focused on the here and now, which is where the issues tend to be.
"I hope he goes on for a long time to come."