The accusation by a female employee of the Red Bull team has left Horner's fate at the team he has led to seven drivers' championships and six constructors' titles hanging in the balance.
Red Bull's parent company, the Austrian drinks giant, have set up an independent investigation, with Horner subjected to an eight-hour grilling by a lawyer in London on Friday.
With a verdict reportedly not expected imminently, it means the reigning world champions will launch their 2024 car on Thursday with the damaging affair hanging heavy in the air.
"My advice to Christian, apart from keeping his head down, is to do nothing, wait and see what happens," Ecclestone told AFP on Tuesday.
Ecclestone and Horner are friends from the days when Horner first joined Red Bull as the pitlane's youngest team principal aged 31 in 2005.
"I keep in close contact with him," the now-retired 93-year-old Ecclestone said by phone from his home in Switzerland.
"The trouble is once you are successful you make a lot of enemies and this is a case in point.
"I hope Christian keeps his head down and that someone talks individually to him and the woman and it is sorted out."
Ecclestone, who over several decades transformed the sport into a global multi-billion-dollar commercial giant, suggested that since the death of Red Bull founder Dietrich Mateschitz in 2022 Horner had become something of a target.
"I feel when Dietrich died it created a vacuum and several people moved into different positions and saw an opportunity to make up all sorts of stories and hurt him (Horner) so they can engineer his departure and create an opening for themselves," he said.
"Effectively they want to oust him."
Ecclestone holds Horner in high regard, and clearly hopes one of F1's lead characters can ride it out
"He has been responsible for a huge run of success and done an incredible amount of good not just for the team but for the sport."
