Thailand's army declared martial law to restore order after six moths of street protests that have left the country without a proper functioning government, but denied that it was staging a military coup.
The baht earlier fell as much as 0.5 percent to 32.62 per dollar, but it recovered most of its initial losses with the central bank suspected of intervening to support the currency.
Bangkok shares fell nearly 1 percent, while government bond yields rose.
Still, analysts did not expect a significant exodus of foreign funds unless violence escalates and threatens further damage to Southeast Asia's second-largest economy.
"The baht could slowly weaken towards 30.00," said Saktiandi Supaat, head of FX research at Maybank in Singapore.
"But capital outflows may be limited as all political problems were priced in already and there have been value buyers into Thailand."
Despite prolonged political unrest, the baht has risen 1.2 percent against the dollar so far this year, according to Thomson Reuters data.
The rupiah fell in both local and non-deliverable forwards markets as Indonesia's presidential election on July 9 turned into a tight race.
On Monday, the country's second-largest party suddenly switched its support away from frontrunner Joko "Jokowi" Widodo to his main rival, former general Prabowo Subianto.
Indonesian shares lost ground with a more than 2 percent slide, while most government bond yields rose.
The official Jakarta Interbank Spot Dollar Rate, which Indonesia's central bank launched last year in an effort to manage exchange rate fluctuations, was fixed at 11,441 per dollar, much weaker than the previous day's 11,351.
"We will see persistent profit-taking," said Yuna Park, a currency and bond analyst at Dongbu Securities in Seoul.
"The political risks are likely to prevent fresh investment as economic reforms and recovery will be delayed," Park added.
The rupiah was the best-performing Asian currency so far this year with a 6.3 percent gain due to prospects of a straightforward victory for Jokowi in the presidential election.