Tsitsipas, the world number 12, took the first set in Tokyo but had no answer to his 49th-ranked opponent for the rest of the match, losing in 1hr, 48min.
Tsitsipas, a two-time Grand Slam finalist, also lost in the first round of the US Open last month.
He announced last month that he was ending his long-time coaching collaboration with his father Apostolos.
Tsitsipas said after losing to Australian Thanasi Kokkinakis at the US Open that he was "nothing compared to the player I was before", speaking of "long-term burnout".
The former world number three has slipped out of the top 10 and has won just two titles in two seasons.
Michelsen was joined in the second round at the Japan Open by Britain's US Open semi-finalist Jack Draper, who beat Italian qualifier Mattia Bellucci 6-4, 6-2.
American Tommy Paul, the number five seed, beat Italy's Matteo Arnaldi 6-3, 6-2.
Japan's Yoshihito Nishioka edged Canada's Felix Auger-Aliassime 7-6 (7/5), 3-6, 7-6 (7/5) in a match that lasted 3hr, 12min.
