It is thought to be the first time anyone has successfully sneaked into Aung San Suu Kyi's compound or swam across the lake in an attempt to get there.
More than 20 police entered Suu Kyi's compound on Thursday morning, according to neighbours who spoke on condition of anonymity.
The house is monitored by heavy security with checkpoints and barbed-wire barricades, but police rarely enter the actual compound where she has been kept under house arrest for more than 13 of the past 19 years.
She is not allowed visitors, apart from her doctor and occasional meetings with party officials, and has not been seen in public for many months.
The Myanma Ahlin report said Yeattaw had confessed to swimming across the lake on Sunday evening, entering Aung San Suu Kyi's house and stayed there until Tuesday night.
Police confiscated the man's belongings which included an American passport, a black backpack, a pair of pliers, a camera and two $100 bills, the newspaper reported.
A spokesman from the US embassy in Yangon confirmed Yeattaw's arrest and said consular officers were "seeking access'' to him.
"Right now we don't know anything more than what is generally known, that this man was arrested for swimming across the lake and wound up being at Aung San Suu Kyi's house," Richard Mei told the Associated Press.
Aung San Suu Kyi has been held without trial for leading a democracy movement in Myanmar, which has been ruled by the military since 1962.
Her National League for Democracy (NLD) party won Myanmar's last elections in 1990, a result the government never recognised.
Aung San Suu Kyi's current period of house arrest is due to end on May 27, but earlier this week NLD officials said an appeal to free her had been rejected by the military government.