At around 6 a.m. he was seen walking around the lake with his entourage, waving to people. Several locals returned the gesture.
He walked for around 25 minutes before getting back to the car and returning to his hotel, Vietnam News Agency reported.
Suga and his wife arrived in Hanoi on Sunday night for a three-day official visit, his first foreign trip after taking office last month.
His predecessor, Shinzo Abe, too had chosen Vietnam as his first foreign destination.
At a news conference Monday following talks with Prime Minister Nguyen Xuan Phuc, Suga promised emergency assistance for the severe flooding in the central region and to share Japans' experience in coping with natural disasters.
The two PMs signed 12 memorandums related to the economy, environment, public infrastructure, healthcare, agriculture, and energy.
Suga leaves for Indonesia on Tuesday.
The 71-year-old took over as prime minister after Abe resigned citing health problems.
Vietnam and Japan established diplomatic ties in 1973 and upgraded them to a strategic partnership in 2009 and to an extensive strategic partnership in 2014.