Ricciardo has suffered a break to the metacarpal in his left hand following a Turn 3 FP2 crash at Zandvoort. The impact with the barriers appeared to rip the steering wheel out of his hands.
Red Bull reserve and Japanese Super Formula championship challenger Liam Lawson will deputise for Ricciardo for the rest of the Dutch GP weekend, while the Italian round follows immediately after.
After a one-week break, the season resumes in Singapore. Red Bull F1 boss Horner reckons this is the event Ricciardo - whose comeback after being sacked by McLaren only started in Hungary - has in mind for his return.
He told Sky Sports: “That's the thing he was most frustrated about, talking with him last night.
“He's just taken a bunch of time off, just getting his mojo back, getting back into it and now he's on the bench again. That was, I think, his frustration.
“I think he felt that the car, they've started to make some progress and it's a shame for him.
“But I'm sure, at the back of his mind, he's probably got Singapore as a target.
“But then again, Singapore is probably one of the most tough circuits on the calendar. But nature will take its course.”
Horner added that Ricciardo had departed Zandvoort to undergo surgery in Barcelona as soon as Sunday. It is understood that he will be, in part, treated by Doctor Xavier Mir.
Mir operated on Lance Stroll following the cycling crash that ruled him out of pre-season testing in Bahrain. The Aston Martin driver then contested the season opener a week later.
Horner explained: “These guys, we see it in MotoGP, they bounce back pretty quick so he's headed off today to Barcelona.
“They may even have a little operation on him tomorrow to just tidy up where that break is.
“It's quite a clean break and then, of course, it's all about the recuperation and how long that takes.
“Any normal human being would probably be about 10 to 12 weeks, but we know that these guys aren't normal.
“So, it will all be about the recovery process - how long that will take, is it going to be three weeks, a month, is it six weeks? Nobody really knows.”