Technically none unless stated by the program; if you are asking about getting into a program vs getting a job afterward. I have zero and got into two programs, one requiring 2 years in the chosen field. There are plenty of programs out there for NP so I don't think it's a problem for you at all.
Now, real world? I'm sure the nursing profession would rather you get at least a year in med/surg or the like so you know some things or ob/peds if you want midwife.
I've got a decade of clinical and orthopedic experience but as a D.C. so it's not nursing but an exam is an exam, labs are labs and diagnostics are...blah, blah...regardless of what some people want to argue.
I have only worked in CT surgery and am in my second year of my FNP program. I'm in CTICU now, and while it helps me for CV and understanding some disease processes more, I wish I had some ED/urgent care experience. That would better replicate having someone come in with no diagnosis and you're gathering the history and triaging and seeing a diagnosis formed. However, I don't want to have the stress of a job change in the midst of the program so I'm sitting where I am. I'm sure my training on Tandem Hearts and balloon pumps and all that jazz will be very very helpful as an FNP : )
An ICU is nice in that you tend to have more dialogue with the providers, and more time to delve into your patient assessment and their hospital course and labs etc. But really it's a different ballgame from primary care.