The municipality refused to grant the couple's citizenship application due to 'their lack of respect for gender equality' Lausanne mayor Gregoire Junod said.
He said a municipal commission had questioned the couple several months ago to determine if they met the criteria for citizenship, but had determined in the ruling made public Friday that they missed the mark on integration.
He did not to divulge the couple's nationalities or other identifying details, but said they 'did not shake hands with people of the opposite sex.'
They also 'showed great difficulty in answering questions asked by people of the opposite sex,' he said.
Some devout Muslims argue that Islam does not permit physical contact with a person of the opposite sex, with the exception of certain immediate family members
Junod pointed out that freedom of belief and religion is enshrined in the laws of the Canton of Vaud, which encompasses Lausanne, but 'religious practice does not fall outside the law,' he stressed.
His vice-mayor, Pierre-Antoine Hildbrand, who was on the three-member commission that questioned the couple described himself as 'very satisfied with the decision' to deny the couple's application.
'The constitution and equality between men and women prevails over bigotry,' he said.
The couple now has 30 days to appeal the decision.
This is not the first time refused handshakes have stirred tensions in Switzerland.