He added that he and his wife were “still immature in many ways, but we would appreciate your kind support”.
Ohtani, nicknamed “Sho-Time”, has achieved stratospheric fame in Japan and abroad.
Known for his skills as a pitcher as well as a batter, he helped Japan win last year’s World Baseball Classic.
Ohtani left the Los Angeles Angels last year for free agency after failing to reach the MLB playoffs.
Following weeks of frenzied speculation, he joined the Dodgers in December. His 10-year deal worth US$700 million was the richest contract in the history of North American sport.
He made his Dodgers pre-season debut on Tuesday, smashing a home run in his new team’s win over the Chicago White Sox.
In his Instagram post, Ohtani said he would hold a press conference on Friday, asking the media to refrain from approaching his wife or her family members.
“Who in the world is the lucky lady? Congratulations,” businesswoman Junko Ito, 33, told AFP in Tokyo.
“He has someone supporting him on the sidelines. I will cheer for him even more,” she said.
But 22-year-old amateur baseball player Akito Suzuki said he was “shocked and saddened” by the news.
“Now he is married, there’s no chance for me. I feel a bit bitter. I wanted him to be mine,” he said, bemoaning how Ohtani had kept his private life quiet until now.
Born in northern Japan, Ohtani was a high-school baseball prodigy who initially wanted to skip the domestic league and head straight to the majors.
Instead, he signed with the Hokkaido Nippon-Ham Fighters in 2013 and spent five seasons there before joining the Angels.
Ohtani’s every move is headline news in Japan, with his achievements a matter of national pride. His marriage announcement was quickly splashed across Japanese media outlets.