Are there post-doc grants available for non-US citizens in the US? I was looking for postdoctoral grants/fellowships for a potential post-doc opportunity in the US. It appears as the entire grant/fellowship system is geared towards US citizens, or permanent residents of the US. It is understandable with respect to use of federal resources, but slightly discouraging nevertheless.

Are there any funding opportunities available for non-US citizen? In terms of field I'm interested specifically in Biomedical and STEM fieds.
There is relatively little funding of the sort you are looking for--funding that non-U.S. residents can apply for directly to fund post-doctoral work inside the U.S.  However, that is not really that important, since that is not how most post-doc positions are funded anyway.

Most post-docs do not apply for their own funding.  The funding comes from the institution that hires the post-doc (Very often--but not always--the money ultimately comes from a research grant from an outside agency, but the post-doc would not be involved in writing or administering the grant.)  If an institution has funds for a post-doc, they will advertise a job opening and hire somebody.  Generally, the search is global; they would be willing to hire somebody from anywhere in the world, provided they are a qualified.  (There are some technical caveats about how this works, but they are of little import in practice; and--again--they are things that the hiring institution mostly needs to worry about, not the person they choose to hire.)