I'm in a phase of hiring at the moment. I would say the length per se is something of a red herring, but to rephrase your question slightly, absolutely it is offputting, and likely to lead to not getting an interview, if your resume doesn't include sufficient information to enable an informed decision. And yes, I have binned candidates due to their not having given me enough data to make an informed decision, especially where that co-incides with no explanation in any form (cover note, email message, resume body) of how the candidate meets the advertised criteria.
You need to include data that lets the hiring manager know that you meet all the threshold requirements (some of which might be unstated - such as 'sufficient grasp of English written communication'), and data that convinces the hiring manager that there are ways in which you are superior to other candidates who meet all the threshold requirements. Unless you know the other candidates personally (may be possible in a niche professional job, where the number of candidates meeting the criteria is very low, and you have likely met them at professional events - e.g. judgeship, senior surgeon - but unlikely elsewhere) there is going to be some redundancy in your resume, because you can't completely anticipate how the other candidates are presenting themselves. Excepting jobs where the requirements are 'have a pulse, and get to the site reliably', it's difficult to imagine less than one page getting those jobs done.
That said, if your current role is very prestigious, and you have a very strong reputation in your industry, you may occasionally get away with a very short resume. You can imagine, for example, that if Stephen Hawking had wanted to switch from Cambridge to Oxford or maybe Princeton some time in the last 35 years, once he'd convinced them he was the 'real' Stephen Hawking, the details on a resume wouldn't have had much to do with the decision (not saying that getting the job would be certain - just that any plausible interviewer would be thoroughly familiar with Hawking's work and able to make a decision).
To summarise, be sceptical if your resume seems very short. Imagine you're the hiring manager - is every thing you would want to know written on the resume, including ways you are different to other candidates (for example, if you are applying for a graduate position, having a degree doesn't make you different)? If necessary, put it aside and come back to it the next day, so that important information is not omitted.