Police said they made the arrest in Rorschach, a town eight kilometres away, near Lake Constance, shortly before 11 pm.
A 74-year-old Italian man died from gunshot wounds on the Wiesenstrasse around 5.40pm, while his 67-year-old wife was seriously injured from the shooting, police said.
A Rega rescue team transported the woman to a hospital in a helicopter but she died of her injuries.
Witnesses reported that a man who shot the couple fled in a grey Mazda 323, police said.
Officers later found the abandoned getaway car on the A1 Highway heading towards the city of Saint Gallen.
Local prosecutors launched a criminal investigation and police are not commenting further.
The shooting shocked residents of Saint Margrethen, a normally placid town of 5,660 people, with a large foreign population, which is otherwise known for its historic church.
The 20 Minuten newspaper reported online that a neighbour said he saw the Italian victims returning from a supermarket in their car to the apartment building where they lived.
When the car was in front of a garage, a man leapt out of another car and fired several shots at the couple, he said.
The neighbour saw the Italian man get out of his car and walk several steps before falling down, 20 Minuten reported.
“I tried to help him and to revive him but without success,” he said.
Another neighbour said he heard four shots fired, according to the online news site.
20 Minuten reported that, from information given by neighbours, the Italian man who died worked as the caretaker of the apartment building for 30 years.
Blick reported online that neighbours said his wife worked at a Migros store.