General opinion seems to be that it's some type of man-made fibre, ie a rayon manufactured from plant material, but there are so many different brands.
The original 'art silk' dating from the late 19th century was rayon manufactured from wood pulp dissolved in cupromonium and sodium hydroxide (caustic soda). Modern brand names include Cupro and Bemberg.
Soon afterwards came viscose rayon where the wood fibres are dissolved in carbon disulphide and sodium hydroxide. Modal is the biggest modern brand name.
Lyocell developed in the 1970s is a rayon where the cellulose fibres are dissolved in N-Methylmorpholine N-oxide in a 'closed loop' process whereby the chemicals are not released into the environment meaning that it's more eco-friendly although it does use a lot of energy. Brand names include Tencel.
LyocellNowadays it's not always wood pulp that's used for man-made fibres, bamboo and even sea-weed can be used
@Diane Because it's soft and doesn't crease my guess is that your blouse is of the lyocell variety