The pair, aged 58 and 59, from Linz in the north of the country, were having breakfast when the illicit parcels were delivered to their home.
At first, they believed the boxes contained two dresses ordered online from the Netherlands.
But instead they found one of the cases contained €500,000 worth of ecstasy, or MDMA, tablets.
A later investigation found the package was intended for a Glasgow address.
A search warrant was carried out at a premises in Glasgow but no arrests were made.
A translated statement from the Upper Austria Police said: "The originally planned cosy breakfast was quickly over and the horror was great, as it turned out that in the second package was about 24,800 Ecstasy tablets worth about 500,000 euros."
The drugs arrived in cardboard boxes, filled with three bags packed with pink tablets.
The woman initially believed the colourful pills were decorative stones, but her husband realised they were probably drugs and immediately returned them to the local post office.
The police added: "There too, the astonishment about the content of the package was great, which is why the City Police Command in Linz was informed.
"In the following investigation it turned out that it was a mail misconduct - the package should have been actually sent from the Netherlands to Scotland."
A National Crime Agency spokesman said: "This is a live investigation and enquiries are on-going."