Ecclestone's 40-year reign as supremo of the sport is currently undergoing its toughest period, with the 82-year-old involved in a High Court case and also potentially awaiting trial in Germany.
"Bernie is a unique individual who has run Formula One tremendously successfully for the last 40 or 45 years," said Horner.
"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."
In London, German media group Constantin Medien is claiming damages of 171 million US dollars (£111million), claiming the 47.2 per cent stake in the sport previously owned by bank Bayern LB was sold too cheaply in 2006 to the current stakeholders, private equity firm CVC Capital Partners.
In an agreement with Bayern LB, Constantin Medien was entitled to a share of Bayern LB's proceeds from the sale.
In Germany, Ecclestone was recently indicted with regard to a 44million US dollars (£29million) payment made to a banker to help smooth the sale of F1 to CVC.
Ecclestone claims he was being "shaken down" by Gerhard Gribkowsky, previously Bayern LB's chief risk officer and who managed the sale.
Gribkowsky was imprisoned last June for eight-and-a-half years after being found guilty of breach of trust, tax evasion and receipt of corrupt payments.
Prosecutors in Gribkowsky's trial claimed he sold the stake without updating its valuation in return for bribes disguised as consulting contracts.
Ecclestone claims the money was paid to avoid particular financial dealings being exposed by Gribkowsky to the Inland Revenue with regard to an offshore family trust known as Bambino Holdings.
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."
It has previously been suggested as a close friend of Ecclestone, Horner could be the man to eventually be his successor.
When asked whether Ecclestone had sounded him out about the prospect, Horner 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."