The Straits Times understands that the deceased is Melisa Liu Rui Chun, 34. Her husband Ng Su Teck, 35 was injured by glass shrapnel.
Shanmugam said Singapore strongly condemns the "heinous attack", which left over 20 people dead and 120 injured so far.
"We have all been deeply shocked by the bombing in central Bangkok yesterday... Members will join me in extending our deepest condolences to the family to the young lady who was killed," Mr Shanmugam said.