So there are only a few online programs with some notoriety. University of Cal Berkeley's MFE is ranked inside the top 5 in the nation (depending on which poll you look at) and is the only program inside the top 10 to offer their degree online.
University of Washington and Johns Hopkins both also have fully online MFEs, but neither have great name recognition within Financial Engineering.
The Cal Berkeley application standards are the same for the part-time online as for the full-time, so the criteria is pretty thorough (2 letters of rec, GRE if you don't have a PhD or didn't finish your undergrad with 3.75/4.0 or greater, two written essays, video essay and finally an interview by a former alumn if you make it past the initial screening). Just like most MFEs these days, they also want you to have a solid quantitative background in your undergrad (or show the capability to learn it) as well as machine learning, stats and programing (either C++ or Python or both).
U Wash and Johns Hopkins are very straightforward and accept almost anyone that applies and has some STEM background or even finance, econ, etc.
Hope that helps.