Breen was set to pilot the team's third car at the asphalt event which would have marked his second WRC outing of the year after rejoining the South Korean marque as a part-time driver for the 2023 season.
The 33-year-old Irishman succumbed to injuries sustained in a crash during a pre-event test for the asphalt rally last Thursday. Breen's co-driver James Fulton was unharmed.
Hyundai has announced that it won't field its third i20 N this weekend out of respect and instead will run cars for full-time drivers Thierry Neuville and Esapekka Lappi only.
The decision to participate was reached after careful consideration, which included discussions with Breen's family, his co-driver Fulton, and Hyundai Motorsport's crews and team members.
Prior to the crash last week, Dani Sordo had been confirmed as the driver for Hyundai's third car for the following round in Portugal in May.
Hyundai will run a special livery on its cars to honour Breen. It is widely expected that the WRC and all Rally1 and Rally2 teams will pay tribute with special liveries at this weekend's rally.
"After careful consideration involving all stakeholders, we have decided to participate in Croatia Rally," said team principal Cyril Abiteboul.
"We will do this in memory of Craig, to honour him, his passion for rallying and his competitive spirit. We will enter two cars and withdraw the third entry as a mark of respect.
"Both cars will run with a special livery for Craig, his family, friends and fans. It is clear from speaking to everyone that the best way to honour Craig's legacy was not to withdraw our entry, so we participate mindful of our lost team-mate, friend and incredible competitor.
"We are contesting this rally primarily to honour Craig and his incredible life and talent. Craig was a proud Irishman and passionate representative of the Irish rally community so the livery will represent the colours of the Irish flag in his memory."
Hyundai Motorsport president Sean Kim paid tribute to Breen in a statement issued by the team last Friday.
"The reality of yesterday has still not sunk in, and it is unlikely to for a very long time," said Kim. "Everyone here in Alzenau is feeling the loss of our team-mate and friend Craig deeply, and we are supporting our colleagues through this incredibly difficult time.
"To say he was a much valued and well-regarded member of our team only touches the surface. Craig had a passion for rallying that ran deep. He was more than just a driver, he was a true lover of the sport. Craig wore his heart on his sleeve, something that enamoured him to so many people. He had a way with words that was completely unique; his end-of-stage quotes were always a highlight.
"Craig was also a phenomenal driver. There are so many highlights, both within our team and in the rest of his career, but in Rally Sweden he showed us his true essence. He was performing at the top of his game and reminding us all of the incredible talent he possessed. That podium meant a lot to us as a team, but you could see just how much it meant to him.
"It is clear the whole rallying community and beyond is feeling this profound loss. The outpouring of grief and sadness in the past day is testament to the man that Craig was. He leaves behind a legacy within Hyundai Motorsport and the wider motorsport community that is difficult to put into words. Rest in peace, dear friend."
Breen's funeral is set to take place on Tuesday at 1pm in his native Ireland at The Sacred Heart Church, Ferrybank. The mass will be streamed online for those that are unable to attend.
