Holland said he was told about the issue by the team's staff just before his season-ending address to the media Wednesday.
Bear's girlfriend, Lenasia Ned, posted on social media that the defenseman "received numerous racist messages and comments" in the aftermath of the Oilers' four-game series loss to Winnipeg in the first round of the NHL playoffs.
The Jets tied Game 4 at 3-3 after a turnover by Bear, with Winnipeg eventually winning in triple overtime. The 23-year-old Bear is from the Ochapowace Nation in southern Saskatchewan.
"He's a tremendous role model for all young athletes, especially in the Indigenous community," Holland said. "He gives time to the community. He's popular in the locker room. ... I feel sick for him. I feel disappointed for him that he would he would get this kind of abuse. I think we've made strides, but there's a long way to go to create a world where we're where everybody feels safe and they don't get this kind of racism and abuse."
Holland said he planned to reach out to Bear.
"I'm 65 years old. I don't live in that social media world," he said. "I want to talk to our PR people ... and see what we can do as an organization to try to make sure this doesn't happen in the future."
Bear, with Ned at his side, addressed the situation with a statement in a two-minute video posted to social media later Wednesday.
"I know this doesn't represent all Oilers fans or hockey fans, and I greatly appreciate your support and love during this time. I'm here to stand up to this behavior, to these comments," he said. "I'm proud of where I come from -- I'm proud to be from Ochapowace First Nation. I'm not just doing this for myself; I'm doing this for all people of color. I'm doing this for the next generation, to help make change to love one another, to support one another, to be kind to each other. There's no place for racism in our communities, in sports or our workplace.
"I call on all of us to make change and end racism."
The Oilers followed Bear with their own statement, saying:
"The Edmonton Oilers Hockey Club is equally disappointed in these disgusting, cowardly and racist remarks. While we have witnessed progress in the area of equality and inclusion, this reprehensible behavior demonstrates we still have significant work to do. We call upon everyone in Oil Country to stand up to racism, call out hatred and do their part in making our community one of acceptance, inclusion and respect."
The NHL also released a statement on Twitter later Wednesday.
"Ethan Bear represents both our game and his Indigenous heritage with dignity and pride," the NHL said. "He, and all people from Indigenous backgrounds, deserve to feel empowered and respected on and off the ice. We stand with Ethan and his family in denouncing hate."
The Confederacy of Treaty Six First Nations said in a statement it was appalled by the racist comments.
"We all have a responsibility to speak out against racism in any circumstance, and to ask those involved to stop," Grand Chief Vernon Watchmaker said. "We are mindful that racism is hurtful and this has gone on for far too long."
Oilers captain Connor McDavid showed his support for Bear, as well.
"The racist comments directed at our teammate and our brother Ethan Bear are not acceptable," McDavid said. "The individuals who spew this type of hate should think twice about their behavior. On behalf of all my Oiler teammates, we stand strong behind Ethan and against racism of any kind."
Bear played in 43 games this season, as well as all four postseason games, garnering major minutes on the Oilers' blue line. In the regular season, he averaged 17:58 time on the ice, finishing with two goals and eight points.
The Associated Press contributed to this report.