The Saudi government declined to comment about the chateau to the Times, but has disputed reports that a Saudi royal purchased the da Vinci on behalf of Crown Prince Mohammed.
In light of the anti-corruption arrests, the chateau and yacht purchases send signals that are inconsistent with Crown Prince Mohammed's social and economic reforms, said Robert Jordan, former U.S. ambassador to Saudi Arabia under President George W. Bush.
"The lack of judgement and the lack of self-awareness that this reflects I think is shocking," he told CNBC's "Squawk Box" on Wednesday.
"There will be members of the royal family, others in the community, who are saying, 'Wait a minute. This guy is just the biggest hypocrite in the world.' So, I think he's got to be very careful to balance that," said Jordan, now an adjunct political science professor at Southern Methodist University.
But others say Crown Prince Mohammed's spending habits and his corruption crackdown are separate issues, and those who conflate them might fuel misconceptions about public opinion Saudi Arabia.
Crown Prince Mohammed is trying to rein in widespread corruption, not discretionary spending by the future king, said Bernard Haykel, professor of Near Eastern studies at Princeton University. He says Saudis don't consider splashy purchases to be corruption, nor do they typically object to wealthy princes investing in assets with tangible value like overseas property, yachts or artwork.
"This is not a guy who is going to Monaco and dropping $100 million on gambling," Haykel told CNBC on Wednesday. "That would be a very different kind of story."
While Western media are focused on the purchases, the average Saudi is more concerned about the introduction of a new value-added tax and the ongoing reduction in fuel subsidies, said Haykel, who recently traveled to Saudi Arabia. These Saudis worry that their incomes will not rise to meet higher costs.
Haykel says wealthy Saudis who say they built their fortunes through legitimate channels are "ecstatic" that Crown Prince Mohammed cracked down on allegedly corrupt princes and officials. They see the type of corruption he is targeting, like bribe-taking and skimming funds for development projects, as a burden on the system, Haykel said.
Still, Haykel says Crown Prince Mohammed has not clearly communicated his motives for the crackdown either at home or abroad.