According to Swiss daily Blick.ch, the suspect was arrested at the scene. The Geneva prosecutor's office has detained him, pending enquiries.
The alleged murder took place in the centre of Geneva. The ex-spouses had apparently been arguing for years.
The couple had originally lived, according to media reports, in St. Gallen but then had separated and divorced.
The lawyer had moved to Germany, while the woman and her children moved to Geneva. Swiss authorities had previously imposed a restraining order on the man because of his behaviour towards his ex-wife.
On Saturday night, there was apparently a violent confrontation between the ex-spouses in the house where the women – originally from Mexico – lived with her children. The 35-year-old man allegedly fired four shots in the stairwell of the apartment building. The 42-year-old woman was so badly injured that she died immediately.
Austrian consular representatives in Switzerland have been informed of the case, according to a spokesperson for the Foreign Ministry in Vienna.
"The relevant Austrian citizens will be looked after by the consul," he said.