A neighbour called Vaud cantonal police over a noisy dispute in the Swiss couple’s apartment on Sunday afternoon.
But when officers from two patrols arrived and broke into the apartment they discovered a man speaking incoherently and after a brief search found the woman’s lifeless body, police said.
Police said the initial evidence indicated the woman died from several knife wounds.
The formal identification of the woman remains under way.
The husband was arrested and taken by ambulance to a hospital for various checks.
Police said he was not immediately questioned because of his “psychological state”.
Officers had previously attended the apartment after being contacted over complaints from neighbours of noise.
The local prosecutor’s office is directing an investigation conducted by inspectors into the alleged murder.
Gland is located in the Lake Geneva region between Geneva and Lausanne.
Meanwhile, police in Basel are continuing to investigate the suspected murder of a young woman, found dead in her apartment on the Gundeldingerstrasse on Monday morning.
Who she was and how she was killed remain unclear, the prosecutor's office from the canton of Basel-City said.
According to the initial findings, however, the woman was a victim of violent crime.
Domestic violence is a common social problem in Switzerland, accounting for 38 percent of violent crime registered in police statistics, according to federal government figures.
In 2011, 27 homicides were the result of domestic violence, involving 21 women victims and six men, the federal statistics office said.
According to Swiss police crime statistics, persons of female gender are 3.1 times more likely to be victims of domestic violence than men.