The whole burglary took place in under 20 minutes and the robbers made off with jewellery and cash after holding a gun to the residents' heads, according to reports in Austrian press.
The couple were named as Bernhard Ramsauer, 56, a board member at private bank Semper Constantia, and his wife Cornelia, 53.
Ramsauer believes that the criminals may have got into the €24 million villa through an open window. "My wife and I were watching television when suddenly these three men were standing in front of us," he said, speaking to Der Kurier.
The pair were able to free themselves and contact police once the robbers had left, suffering only minor injuries to the wrists where they had been tied to the chairs with tape.
"I recommend anyone who finds themselves in such a situation, not to be a hero. It's different from Hollywood films," said Ramsauer.
The crime took place in western Vienna, on Friday at around 10:15pm. It is the third home invasion of this type to take place this year in the wealthy Döbling district; two weeks ago, an apartment belonging to a Serbian author in Brigittenau was ransacked.
State police are investigating, but have no leads on either crime. Police said that there is heavy surveillance and use of patrols in the area due to the high rate of burglaries.
Last week, a gang which had broken in to nearly 6,000 cellars in Vienna was arrested after being caught in the act.
According to police statistics, there are on average two burglaries every hour in Austria.