Amniocentesis involves inserting a long needle through the mother's abdomen and drawing fluid from the womb.
The procedure carries a small risk of miscarriage or infection as well as being uncomfortable. Approximately one in 100 women who have the test will miscarry as a result, according to the Royal College of Obstetricians and Gynaecologists.
The new technique allowed scientists to pinpoint signs of chromosomal abnormality in a study of 18 pregnant women.
Down's syndrome occurs when a foetus has three copies of chromosome 21 instead of two. It can cause physical and intellectual impairments.
If a foetus has three copies of chromosome 21 rather than the normal two, there will also be a relative increase in the quantity of chromosome 21 in the mother's blood.
Professor Stephen Quake, from Stanford University, California, who led the new study, said: "Non-invasive testing will be much safer than current approaches.
"The earlier you know you've got a foetus with Down syndrome, the better able you are to prepare."
Carol Boys, chief executive of the Down's Syndrome Association, told BBC news: "There is no question that these non-invasive tests will be introduced in the next few years.
"It's therefore incredibly important that potential parents are given accurate information on Down's syndrome before they make a choice about whether to terminate or not.
"We don't consider Down's syndrome a reason for termination but we recognise that bringing up a child with Down's syndrome isn't right for everyone."
The research is reported in the journal Proceedings of the National Academy of Sciences.