The stars' private security detail kept journalists at a distance, and one government official warned Saturday that any foreign paparazzi found working without official approval would be kicked out of the country.
Immigration officials confirmed that the couple and five other people, including two children, arrived in Walvis Bay on Monday morning on a chartered jet from Paris, prompting speculation their baby will be born in Africa.
Mark Bongers, an advertising executive, said he expected their visit to be good for business.
"It puts Namibia in the spotlight as a tourist destination, but people mustn't go too crazy about it," he said. "I would imagine that they would like a bit of privacy, and I think if people here screw it up for them, then maybe they won't come back."
Media reports have said that the couple has rented all 14 rooms and suites at the Burning Shores resort, a luxury boutique hotel near the famous dunes of the Namibian desert.
A receptionist reached by telephone at The Burning Shore denied that the couple was there, saying the hotel heard they had gone to Cape Town, South Africa.
Pitt's publicist said Jan. 11 that Jolie is pregnant with Pitt's child. It was unclear when the baby was due.
Jolie has traveled to Africa frequently to shoot films and as a U.N. goodwill ambassador. She spent several weeks in Namibia in 2002 while shooting the film "Beyond Borders."
Jolie has called the continent one of hope and possibility, and adopted a daughter, Zahara, from Ethiopia last year. She also has a son, Cambodian-born Maddox, adopted in 2002.