Aung San Suu Kyi, the leader of the main opposition National League for Democracy (NLD) party, faces up to five years in jail if found guilty.
She has already spent 13 of the past 19 years in detention, most of them at her house on Yangon's Inya Lake.
The 63-year-old Nobel laureate, who was questioned for 25 minutes, also told the court she did not inform the military authorities about Yettaw's intrusion.
"I allowed him to have temporary shelter," Aung San Suu Kyi said when asked about claims that she had given Yettaw food and let him stay.
She said Yettaw left at 11:45pm on May 5, adding: "I only knew that he went to the lakeside. I did not know which way he went because it was dark."
Her testimony will continue on Wednesday.
Yettaw, a Vietnam war veteran from the US state of Missouri, is alleged to have visited her home twice, swimming across Yangon's Inya lake to avoid security.
He was arrested in early May as he attempted to swim back from the second visit.
On Monday, prosecutors abruptly dropped the nine remaining witnesses they had planned to call, fuelling speculation that the trial could end within days.
Nyan Win, one of four lawyers representing Aung San Suu Kyi, told reporters: "If the hearing continues like this, the entire process will come to an end in three or four days."
On Tuesday, the government allowed international diplomats and local journalists inside the special court near the former capital for at least part of the day.
"It's very firm and clear to us that their prime goal is that Aung San Suu Kyi continues to be under detention"
Khin Omar, Burma Partnership
Journalists and diplomats, including a reporter for The Associated Press, were allowed into the courtroom for Tuesday's session, the second time during the trial that such rare access has been granted.
"Thank you for your concern and support. It is always good to see people from the outside world," Aung San Suu Kyi told reporters and diplomats before being escorted out of the court by four policewomen.
Khin Omar, of the Burma Partnership, told Al Jazeera the military leaders made "small concessions" including allowing journalists to attend the trial after feeling the pressure from the region.
"It's very firm and clear to us that their prime goal is that Aung San Suu Kyi continues to be under detention," she said, adding that many in Myanmar were quietly praying for her release.
She will be followed by testimony from four defence witnesses, including Win Tin, Myanmar's longest-serving political prisoner until his release last year, and Tin Oo, the vice-chairman of the NLD.
The charges against her are widely considered a pretext to keep her detained ahead of elections the military government has planned for next year as part of its "roadmap to democracy".
But critics say the regulations surrounding the election mean it will only cement continued military control, which the country has been under since since 1962.
It last held an election in 1990, but the government refused to recognise the results after a landslide victory by the NLD.