But Aung San Suu Kyi, who has been under detention for 14 of the last 20 years and was sentenced to a further 18 months of house arrest for Yettaw's stunt, criticised the military government's double standard on Monday.
"The fact that the person who entered the house was released whereas residents of the house remained detained is ugly," Nyan Win, her lawyer, quoted her as saying.
Phillip Crowley, a US state department spokesman, said Yettaw's release could not be seen as an indication that Myanmar, formerly known as Burma, was embracing change.
"We remain very concerned about the continued detainment of Aung San Suu Kyi and more than 2,100 prisoners that are in detention,'' Crowley told reporters on Monday.
"We'll be looking for signs that Burma's fundamentally changing its approach and its policies."
During his visit last week, Webb met Senior General Than Shwe, Myanmar's military chief, before visiting Aung San Suu Kyi at a guest house.
Ban welcomed Webb's "engagement with Myanmar's leaders as well as Daw Aung San Suu Kyi towards a peaceful, united, democratic Myanmar", his spokeswoman, Marie Okabe, said on Monday.
Ban himself met Than Shwe on a visit to the country's capital Naypyidaw last month, but was not allowed to meet Aung San Suu Kyi.
Myanmar state television said Yettaw, who was held for three months in a Myanmar jail during his joint trial with Aung San Suu Kyi, was freed on humanitarian grounds because of his poor health.
He suffers from diabetes and was hospitalised for a week during the trial after suffering seizures.
On Sunday, Webb arrived with Yettaw in Bangkok, where he has been receiving medical care.
"Our first priority is ensuring the health of Mr Yettaw," Cynthia Brown, a US embassy spokeswoman in the Thai capital, said.