She attended Radcliffe College, where she received her AB in 1960. In 1963 she received her Ph.D. from Harvard University. Since 1969 she has taught at the University of California, Los Angeles.
Greibach is well known for her work on formal languages. One of her contributions is Greibach normal form, a normal form for grammars in which every production is of the form A -> aB or A -> a.