The lives of the victims are not in danger but they remained in hospital on Wednesday for treatment of severe burns.
The attack took place on Monday evening outside an apartment building in Grand-Lancy, Geneva cantonal police said.
Carrying the acid in a cup, the attacker poured the liquid over his former girlfriend and in the face of her new partner, police said in a news release.
The woman suffered third-degree burns on parts of her body, police said.
Ambulance attendants treated the couple before transporting the pair to hospital.
Officers tracked down the attacker at his home.
Police said he refused to make any declaration about the incident, which is now under investigation by Geneva authorities.
Le Matin newspaper cites sources indicating that the woman, 39, suffered burns all over her body while her partner risks losing the sight of one eye.
A neighbour described the alleged assailant as an “unremarkable guy who had a dog”.
But a source said the woman complained that she had previously been threatened by the man with whom she has a 15-year-old son, the newspaper said.