The current member of parliament and former industry minister, 73, is said to be one of the more hardline members of the Union Solidarity and Development Party founded by former military strongman General Than Shwe and now led by President Thein Sein.
The US Treasury sanctions freeze any US-based assets he might have and ban Americans from doing business with him.
But the US stressed the sanctions apply to Aung Thaung alone, and not to any government organization with which he is associated.
"As the United States continues to support and monitor Burma's reforms, including democratic reform and the national peace process, we remain concerned that certain individuals have been working to counter these efforts."
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The move comes as Myanmar's parliament agreed to consider changing the country's constitution to allow opposition leader Aung San Suu Kyi to run for the presidency next year.
The current charter bars her from being president, yet her National League for Democracy (NLD) party is considered likely to win the polls in 2015 if they are free and fair.
It believes revising the clause will open the way for further changes to other constitutional provisions, including the ring-fenced proportion of soldiers in parliament and the effective bar on Suu Kyi becoming president.
Suu Kyi is currently ineligible because of a clause in the 2008 charter blocking anyone whose spouse or children are overseas citizens from leading the country. The Nobel peace laureate's late husband was British, as are her two sons.
Elections, which are seen as a key test of democratic reforms under the quasi-civilian government.