The three-time World Series champion, 43, is recovering after surgery, the Red Sox said in a statement.
"David's family has confirmed that he sustained a gunshot wound to the lower back/abdominal region," it added.
"We have offered David's family all available resources to aid in his recovery and will continue to keep them in our hearts."
Dominican National Police spokesman Felix Duran Mejia told CNN the incident occurred at the Dial Discotheque in Santo Domingo, where he was born.
Ortiz, a designated hitter and first baseman, ended his 20-year Major League Baseball career in 2016, when he earned the last of his 10 All-Star appearances.
He helped Boston win a first World Series title in 86 years 2004, as well as championships in 2007 and 2013.
"Anxiously waiting for more news. In the meantime, only prayers for David, Tiffany and their family," said former New York Yankees star Alex Rodriguez on Twitter.