Yettaw is also standing trial, along with two female aides who live with Aung San Suu Kyi.
The opposition leader said she first knew of the visit by Yettaw when her assistant woke her up around dawn to tell her that a man had arrived at the house.
Yettaw said he swam across a lake to the house to warn her of a vision he had that she would be assassinated.
Obama said it was "time for the Burmese government to drop all charges against Aung San Suu Kyi and unconditionally release her and her fellow political prisoners".
The case has drawn widespread international condemnation of Myanmar's military government.
Opposition supporters and Western governments critical of Myanmar have condemned the trial, labelling it a pretext for the ruling generals to keep Aung San Suu Kyi in detention beyond national elections it has scheduled for next year.
The government says the vote will mark the culmination of Myanmar's "road map to democracy," but critics say the regulations surrounding the election mean it will only cement military rule.
Myanmar, formerly known as Burma, has been under military rule since 1962.
It last held an election in 1990, but the government refused to recognise the results after a landslide victory by the opposition National League for Democracy (NLD), led by Aung San Suu Kyi.
In court at the Insein prison in Yangon on Tuesday, Aung San Suu Kyi testified that she had not breached the restriction order keeping her at her crumbling lakeside residence.
House arrest 'over'
The Nobel Peace laureate, who has been under detention for 13 of the last 19 years, faces up to five more years in jail if convicted of the latest charge.
Myanmar authorities informed Aung San Suu Kyi on Tuesday that her six-year period of house arrest was officially over – but she continued to be held at Insein prison, her party said.
"We don't know whether we should be happy or sad, because she is still in detention on these charges," said Nyan Win, one of her lawyers and spokesman for the NLD.
"I cannot guess the verdict but according to the law she should be completely free."