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.

Kevin Paddick, 34, of Rosemary Road, Clacton, Essex, is accused of killing Danny Myers, 23, from Enfield.
Mr Myers died in hospital after he was stabbed at an address in Rochford Road, St Osyth, in the early hours of Monday.
The accused is expected to appear before magistrates later. A 29-year-old woman from Clacton, who was arrested on suspicion of murder, has been released without charge.

A rare magnitude-four earthquake hit Greenland's west coast on Sunday, producing a surge of water that swept away homes and led to reports of a number of people missing.
Joint Arctic Command, the group tasked with the search and rescue mission, has since published images of the aftermath of the disaster and told the BBC that it continues to monitor the situation, warning that further incidents could take place.
Homes were submerged and washed away after a tsunami hit the village of Nuugaatsiaq, north-western Greenland.
Rescuers used liferafts to sweep the area after four people were reported missing.
A number of injuries were also reported after 39 people were evacuated from Nuugaatsiaq.
The surge of water is believed to have swept away 11 homes in the small village.
The authorities said the tsunami was caused by a magnitude-four earthquake, which is rare for the area.
Police chief BjÃ¸rn Tegner Bay said he was unable to confirm whether there had been fatalities.
Meteorologists said it was "not normal" for such an earthquake to hit Greenland and warned of aftershocks.

They include her chauffeur in Paris, Michael Madar. The three were among 17 people arrested in co-ordinated raids across France on Monday.
The driver's brother is still being questioned by police, reports say.
Kardashian West was held at gunpoint and tied up by the robbers while staying at a hotel in Paris in October.
She was targeted at the exclusive flat near Place de la Madeleine while her bodyguard looked after her sister at a nightclub.
The gang stole €9m (£8m; $9.5m) of jewellery, including a diamond ring valued at around €4m.
The two witnesses to the robbery - Kardashian West herself as well the night-watchman - apparently both told police that their aggressors were men "of a certain age". CCTV footage on the street outside also provided crucial evidence.
"We would expect the people who carried out a job like this to be criminals with a certain degree of experience. They would need the connections to be able to dispose of the jewels once they had got their hands on them," one police source told the BBC.
Throughout the inquiry, police have been investigating whether the gang was tipped off that Kardashian West's bodyguard was not at the hotel residence at the time of the robbery.
Among those arrested on Monday were several figures in their 60s and one in his 70s. The raids took place mainly in the Paris region and at Rouen in the north. An Algerian, identified as 72-year-old Pierre B, was detained at Grasse on the French Riviera.
Although there has been no trace yet of Kardashian West's missing jewellery, police did recover an estimated €300,000 during Monday's raids.
Two Japanese climbers who scaled the Matterhorn in the Swiss Alps have been found dead on the mountain, according to the Japanese foreign ministry.
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A man has been charged with murdering a man who was stabbed to death.
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Greenland profile
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Three people have been released without charge by French police investigating a Paris jewellery robbery that targeted TV reality star Kim Kardashian West.