Officers arrested the suspect on Saturday at the scene after his 42-year-old former spouse died, the Geneva prosecutor's office said in a news release.
The office has detained him, pending enquiries being led by prosecutor Anne Jung Bourquin.
The alleged murder took place in the centre of Geneva, the prosecutor's office said.
The office said it was not making further comment on the affair.
The couple had apparently been arguing for years.
They had originally lived, according to Austrian media reports, in St. Gallen but then had separated and divorced.
The lawyer 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 lawyer allegedly fired four shots in the stairwell of the apartment building.
The victim 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.