He replaces Prince Khaled al-Faisal, who has been made education minister, a move that may revive stalled educational reforms aimed at reducing the influence of religious conservatives, Saudi analysts said.
The appointments were announced in a royal decree carried by state media in the world's top oil exporter, where moves among senior princes are closely watched for their impact on the country's opaque succession process.
Since 2011, a series of deaths, retirements and promotions mean most top government positions held by princes, plus the three top provincial governor jobs, have switched hands after decades with little change.
Analysts have said the changes reflect a desire by King Abdullah, who is thought to be 90, to establish his sons and other allies in key positions for the future.
"Appointing a son of the king to one of the major governorates in the kingdom is noteworthy. He is giving his sons a big chance to have a place in the succession process," said Khaled al-Dakhil, a Saudi political scientist.
He has appointed his son Miteb as minister of the Saudi Arabian National Guard, his son Abdulaziz as deputy foreign minister and his son Turki as deputy Riyadh governor.
Mishaal, the new Mecca governor, was previously governor of Najran province on the border with Yemen.
The job of Mecca governor carries big administrative responsibilities because the province has a large population, as well as symbolic importance through its guardianship of Islam's holiest site and hosting of the annual haj pilgrimage.
Unlike in European monarchies, the Saudi succession does not pass directly from father to eldest son, but has moved along a line of brothers born to the kingdom's founder King Abdulaziz, commonly known as Ibn Saud.
Abdullah's heir is Crown Prince Salman, who is 78. After Salman, most analysts believe only two of Ibn Saud's living sons, Prince Ahmed and Prince Muqrin might have a chance to become king. After that, one of Ibn Saud's hundreds of grandsons must be chosen.
Besides his own sons, Abdullah has also promoted nephews to other top jobs, including interior minister, intelligence chief, Eastern Province governor, Riyadh governor and deputy defence minister.
By moving Prince Khaled to the education ministry, King Abdullah may also be signalling that he intends to revive stalled reforms to the country's creaking school system.
"Khaled al-Faisal was very critical of extremism in our educational system. But fixing education is a hard job that requires years and years," said Jamal Khashoggi, head of a television news channel owned by billionaire Prince Alwaleed bin Talal.
Significant control over education was given to Islamic conservatives in the 1980s to try to placate them after a militant attack in 1979, but they produced generations of young people with more religious knowledge than practical skills.
Saudi Arabian officials often say the biggest long-term challenge facing the world's top oil exporter is to find real jobs for young people who have proved unable to compete with lower-paid expatriates in the local employment market.