The alleged gunman was captured and beaten by a crowd of people at the bar, Bautista said. He said police are waiting until the man undergoes treatment for his injuries before questioning him.
Investigators are trying to determine whether Ortiz was the intended target, Bautista said.
Two other people were wounded, Bautista said, including Jhoel López, a Dominican TV host who was with Ortiz. Bautista said police believe López was wounded by the same bullet.
López was shot in the leg and his injuries were not life-threatening, said his wife, Liza Blanco, who is also a TV host.
Police did not identify the third person or detail that person's injuries.
The Boston Red Sox, in a statement early Monday, said they have been notified by Ortiz's family that the former slugger sustained a gunshot wound to his "lower back/abdominal region" and that he is recovering after surgery.
The Red Sox said they offered the Ortiz family "all available resources to aid in his recovery" and they will continue to keep them in their hearts.
The Dial Bar and Lounge is located in eastern Santo Domingo on Venezuela Avenue, a bustling nightlife district packed with dance clubs and pricey bars that Ortiz is known to frequent. Ortiz, who lives at least part of the year in the Dominican, is often seen getting his cars washed and hanging out with friends including other baseball players, artists and entertainers.
The 43-year-old Ortiz hit 541 homers in 20 major league seasons, including 14 with the Red Sox. He helped lead Boston to three World Series titles and retired after the 2016 season. He was a 10-time All-Star and World Series MVP in 2013.