It is not Hannibal Gaddafi's first brush with European law
The Swiss foreign ministry has protested to Libya over what it called retaliatory measures for the arrest of Muammar Gaddafi's youngest son.
The ministry said Swiss companies ABB and Nestle have been ordered to close their Libya offices and Swiss staff there have been arrested.
Geneva police held Hannibal Gaddafi for two days last week after he and his wife allegedly hit two of their staff.
Demonstrators in Libya have called for oil shipments to Switzerland to be cut.
The demonstrators, from Libya's influential people's committees, also called for Libya to withdraw its deposits from Swiss banks if an apology for the arrest is not forthcoming.
The protesters, outside the Swiss embassy in Tripoli, shouted their demands as well as putting them in a note handed to the embassy.
Switzerland gets much of its crude oil supply from Libya, through a company run by Hannibal Gaddafi.
The Swiss foreign ministry said Libya began retaliating for Mr Gaddafi's arrest when he was released on 17 July.
Flights between Libya and Switzerland have been reduced, Libya has stopped issuing visas to Swiss citizens and Tripoli has recalled some of its diplomats from Bern, the Swiss foreign ministry said in a statement.
"Since July 17, the Libyan authorities have taken a number of worrying retaliatory measures," the statement said.
The ministry also said it had sent a delegation to Libya to explain Mr Gaddafi's arrest and "prevent a crisis between the two countries".
It has advised Swiss citizens not to travel to Libya until further notice.
It is a row that could prove costly to both countries, says the BBC's Imogen Foulkes in Geneva.
Switzerland imports at least half its crude oil from Libya but Libya owns a large oil refinery in Switzerland.
Hannibal Gaddafi and his wife, who is heavily pregnant, were taken into custody on 15 July after the alleged incident at a luxury hotel in Geneva.
The couple face charges of bodily harm, threatening behaviour and coercion. They have denied any wrongdoing.
It is not Mr Gaddafi's first brush with the law.
In 2005 he was convicted by a court in France of assaulting his girlfriend.