A spokesman said both men were in their 60s, but gave no further details.
The men reportedly ran into bad weather as they were coming down the mountain over the weekend.
Last week, the remains of two Japanese climbers who disappeared 45 years ago were found on the Matterhorn, one of Europe's highest mountains.
DNA tests helped identify those remains - the latest to have been discovered with the melting of ice on the mountain.
The 4,478m (14,700ft) Matterhorn has a distinctive pyramid-shaped peak, making it one of the world's most recognisable mountains.
Hundreds of people have died trying to reach the top.
Two Japanese climbers who scaled the Matterhorn in the Swiss Alps have been found dead on the mountain, according to the Japanese foreign ministry.