Nunez, who is friends with Ortiz and shares an agent with the former Red Sox star, told ESPN's Marly Rivera that he spoke with Ortiz on the phone Tuesday, less than two days after the shooting at a club in Santo Domingo.
Although Nunez said he was happy to hear that Ortiz is recovering, he said Dominican players feel "embarrassed" that a "legend" like Ortiz was shot in their homeland.
"Just thinking about the fact that this happened to him in the Dominican Republic, it is unimaginable," Nunez told Rivera on Wednesday. "For us, as Dominican players, it's a very bad image. It is an international shame.
"We feel very embarrassed about what happened to him because he is a legend from our homeland, and this happened to him in our homeland."
Nunez said he was happy to have had the opportunity to speak with Ortiz.
"I'm very pleased that he's already recovering. ... [Ortiz] said to me, 'How are you, homie? How are you doing?'" Nunez said. "I replied, 'Hey, it's not about how am I doing, it's about how you're doing! You tell me!'
"It was just a brief greeting, but it felt good to have the opportunity to talk to him over the phone."
Ortiz's wife, Tiffany, announced earlier Wednesday that Ortiz will remain in the intensive care unit at Boston's Massachusetts General Hospital "for the coming days."
Ortiz underwent emergency surgery Sunday night in the Dominican Republic to repair damage to his intestines and his liver. He was stabilized and then flown to Boston and taken to Mass General, where a second surgery was performed late Monday night.
Authorities say Ortiz was ambushed by a man who got off a motorcycle and shot him in the back at nearly point-blank range around 8:50 p.m. local time at the Dial Bar and Lounge.
The Dominican Republic's chief prosecutor on Wednesday said police have five people in custody, including the alleged gunman, and that others also are being pursued.
Witnesses said the attack was carried out by two men on a motorcycle and two other groups of people in cars, and authorities said the coordinator of the shooting was offered 400,000 pesos (about $7,800) to carry out the crime.
Nunez, who spoke with Rivera before Boston's game Wednesday afternoon against the Texas Rangers, called Ortiz a "very special person" for all Dominican players.
"I feel terrible," Nunez said. "He is an international figure, an icon of our sport. He's someone who's opened so many doors for younger Dominican players and Latinos in general. He always advocates for the best for the Dominican Republic. For young Latinos, he's always there offering you advice. He's a very special person for all of us."